FROM MINING TO UNDERSTANDING: THE EVOLUTION OF SOCIAL WEB USERS DR. MATTHEW ROWE SCHOOL OF COMPUTING AND COMMUNICATIONS @MROWEBOT | M.ROWE@LANCASTER.AC.UK Faculty of Science and Technology Christmas Conference Lancaster University, UK

From Mining to Understanding: The Evolution of Social Web Users 1

Time

Primary School High School University Postgrad Postdoc Lecturing

Our interests develop ‘Offline’

From Mining to Understanding: The Evolution of Social Web Users 2

Time

Primary School High School University Postgrad Postdoc Lecturing

Offline, we develop in terms of both our interests and social networks

And so too do our social networks…

From Mining to Understanding: The Evolution of Social Web Users 3

This also happens ‘online’, on the ‘Social Web’…

From Mining to Understanding: The Evolution of Social Web Users 4

First, Web 1.0

From Mining to Understanding: The Evolution of Social Web Users 5

Then, Web 2.0… the ‘Social Web’

From Mining to Understanding: The Evolution of Social Web Users 6

…to understand how people behave online

…to learn how people shape their identities

…to predict churners (from social networks and

online communities)

…to build better recommender systems

Why study user evolution?

From Mining to Understanding: The Evolution of Social Web Users 7

User Lifecycles, Properties &

Evolution Measures

Predicting Churners

Recommending Items Conclusions

Talk Outline

User Lifecycles 8

From Mining to Understanding: The Evolution of Social Web Users

From Mining to Understanding: The Evolution of Social Web Users 9

Time

Primary School High School University Postgrad Postdoc Lecturing

Novice Users Asking Questions Asking & Answering Questions

Answering Questions

1 2 3 … n

1 2 3 … n

Offline Lifecycle Periods

Lifecycle Periods of a potential Question-Answering System user (conjecture!)

In reality: do not know the labels, however we can split by equal time intervals:

Yet, users non-uniformly distribute their activity across lifecycles

First Action Last Action

Modelling User Evolution: Lifecycles

From Mining to Understanding: The Evolution of Social Web Users 10

1 2 3 … n

1 2 We divide lifetime into equal activity periods

#actions #actions =

s Model the terms used by user u

User Properties in Lifecycle Stages

Model the tastes of the user

Model the actions to user u by other users

Model the actions by user u to other users Term Count

Semantic 17

Web 5

Mining 4

Statistics 3

Item Rating

Alien 4*

Bladerunner 5*

Star Wars 4*

From Mining to Understanding: The Evolution of Social Web Users 11

How can we track the evolution of user’s properties? Solution: use measures from information theory

From Mining to Understanding: The Evolution of Social Web Users 12

Evolution measure 1: Cross-Entropy

that we eschew time-comparative assessments of how a useris changing relative to earlier properties. To inform suchcross-period assessment we examined the users’ in-degree,out-degree and term distributions across lifecycle periodsby computing the cross-entropy of one probability distri-bution with respect to another distribution from an lifecycleperiod, and then selecting the distribution that minimisescross-entropy. Assuming we have a probability distribution(P ) formed from a given lifecycle period ([t, t0]), and aprobability distribution (Q) from an earlier lifecycle period,then we define the cross-entropy between the distributionsas follows:

H(P,Q) = �X

x

p(x) log q(x) (5)

In the same vein as the earlier entropy analysis, wederived the period cross-entropy for each platform’s usersthroughout their lifecycles and then derived the mean cross-entropy for the 20 lifecycle periods. Figure 2 presents thecross-entropies derived for the different platforms and userproperties. We observe that for each distribution and eachplatform cross-entropies reduce throughout users’ lifecycles,suggesting that users do not tend to exhibit behaviour thathas not been seen previously. For instance, for the in-degreedistribution the cross-entropy gauges the extent to whichthe users who contact a given user at a given lifecyclestage differ from those who have contacted him previously,where a larger value indicates greater divergence. We findthat consistently across the platforms, users are contactedby people who have contacted them before and that fewernovel users appear. The same is also true for the out-degreedistributions: users contact fewer new people than they didbefore. This is symptomatic of community platforms wheredespite new users arriving within the platform, users formsub-communities in which they interact and communicatewith the same individuals. Figure 2(c) also demonstrates thatusers tend to reuse language over time and thus produce agradually decaying cross-entropy curve.

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Figure 2. Cross-entropies derived from comparing users’ in-degree, out-degree and lexical term distributions with previous lifecycle periods. Wesee a consistent reduction in the cross-entropies over time.

3) Community Contrasts (Community Cross-Entropy):For the third inspection of user lifecycles and how userproperties change, we examined how users compare with

the platform in which they are interacting over the sametime interval. We used the in-degree, out-degree and termdistributions and compared them with the same distributionsderived globally over the same time periods. For the globalprobability distributions we used the same means as forforming user-specific distributions, but rather than using theset of posts that a given user had authored (Pui

) to derivethe probability distribution, we instead used all posts. Forinstance, for the global in-degree distribution we used thefrequencies of received messages for all users. Given thediscrete probability distribution of a user from a time interval(P[t,t0]), and the global probability distribution over the sametime interval (Q[t,t0]), we derived the cross-entropy as abovebetween the distributions. (H(P[t,t0], Q[t,t0])).

As before we derived the community cross-entropy foreach platform’s users over their lifetimes and then calculatedthe mean community cross-entropy for the lifecycle periods.Figure 3 presents the plots of the cross-entropies for the in-degree, out-degree and term distributions over the lifecycleperiods. We find that for all platforms the community cross-entropy of users’ in-degree increases over time indicatingthat a given user tends to diverge in his properties fromusers of the platform. For instance, for the community cross-entropy of the in-degree distribution the divergence towardslater parts of the lifecycle indicates that users who reply to agiven user differ from the repliers in the entire community.This complements cross-period findings from above wherewe see a reduction in cross entropy, thus suggesting thatusers form sub-communities in which interaction is consis-tently performed within (i.e. reduction in new users joining).We find a similar effect for the out-degree of the userswhere divergence from the community is evident towardsthe latter stages of users’ lifecycles. The term distributiondemonstrates differing effects however: for Facebook andSAP we find that the community cross-entropy reducesinitially before rising again towards the end of the lifecycle,while for Server Fault there is a clear increase in communitycross-entropy towards the latter portions of users’ lifecyclessuggesting that the language used by the users actually tendsto diverge from that of the community in a linear manner.This effect is consistent with the findings of Danescu et al.[2] where users adapt their language to the community tobegin with, before then diverging towards the end.

V. MINING LIFECYCLE TRAJECTORIES

Inspecting how communities of users develop we haveconcentrated on assessments at the macro-level on eachplatform, examining how the social dynamics and lexical dy-namics of communities of users have changed over time. Wenow turn to examining how individual users evolve through-out their lifecycle periods. Understanding how individualusers develop over time in online community platformsallows for churners to be predicted, as we shall demonstratein the following section through our experiments, and also

User properties in period s

User Properties in period s-1

How do the properties differ between time steps? Decrease = similarity between properties

From Mining to Understanding: The Evolution of Social Web Users 13

Evolution measure 2: Conditional Entropy

Pr(c|Du,s

train

) =ave rating(Du,s,c

train

)X

c

02C

u,strain

ave rating(Du,s,c

0

train

)(4)

Based on this formalisation we can assess the relativemean rating score per category for a given user and lifecyclestage. As our item-to-semantic-category mapping function(�) can either map items directly to the categories they areassigned to (�

p

) or to the grandparent categories (�g

) wecan form taste profiles of users using two di↵erent categor-ical levels. Our intuition here was that the former profiletype, formed from directly mapped categories, would leadto sparse profiles due to the greater specificity that the cat-egories denote, while the latter profile type, formed fromtransitively mapped grandparent categories would lead todenser taste profiles. This theory was influenced by the priorwork of Ostuni et al. [6], in which the authors consider onlygrandparent categories aligned to semantic URIs.

5.4 Taste Evolution: Local vs Global Dynam-ics

We now turn to looking at the evolution of users’ tastesover time in order to understand how their preferences change.We are interested in examining for two e↵ects: (i) local dy-namics, the propensity for users to develop in their owninimitable manner; and (ii) global dynamics, where usersexhibit consistent development properties. Given our useof probability distributions to model the lifecycle stage spe-cific taste profile of each user, we apply information theo-retic measures based on entropy judgements capturing: (i)consecutive lifecycle stage development, and (ii) informationtransfer between global taste profiles and the local taste pro-files at one lifecycle stage and the taste profiles of the userat the next stage.

5.4.1 Conditional Category Entropy

By using conditional entropy we can assess the informa-tion needed to describe the taste profile of a user at one timestep (Q) using his taste profile from the previous stage (P ).A reduction in conditional entropy indicates that the user’staste profile is similar to that of his previous stage’s pro-file, while an increase indicates the converse. We define theconditional entropy of two discrete probability distributions,representing taste profiles, as:

H(Q|P ) =X

x2P,

y2Q

p(x, y) logp(x)p(x, y)

(5)

We derived the conditional entropy over the 5 lifecycleperiods in a pairwise fashion, i.e. H(P

2

|P1

), . . . , H(P5

|P4

),and plotted the curve of the mean conditional entropy inFigure 5 over each dataset’s users in the training split, alsoincluding the 95% confidence intervals to show the varia-tion in the conditional entropies. Figure 5 indicates thatMovie Lens users tend to diverge in their ratings and cat-egories over time, given the increase in the mean curve to-wards later portions of the users’ lifecycles, the same is alsoevident for Movie Tweetings, however the increase is moregradual there. Amazon users, however, di↵er by showing areduction in conditional entropy towards later lifecycle peri-ods. Relating this back to our above definition of conditionalentropy, the global e↵ect that we see on Amazon indicates

that users tend to converge in their reviewing behaviour andthat previous profiles allow one to gauge how the user willrate items in the future given their category information.Conversely, for MovieLens and Movie Tweetings we see anopposite e↵ect: users’ taste profiles become less predictableas they develop; users rate items in a way that renders un-certainty in profiling from previous information.

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(c) Amazon

Figure 5: Parent category conditional entropy be-tween consecutive lifecycle stages (e.g. H(P

2

|P3

))across the datasets, together with the bounds of the95% confidence interval for the derived means.

5.4.2 Transfer Category Entropy

Earlier we postulated that the local development of a userand the global development of all users will have di↵erentinfluential e↵ects on certain users, i.e. influencing how theymay review things. We can examine for such e↵ects underthe premise that local development and global developmentare two di↵erent systems, although the former contributesto the latter we would expect a given user who is influencedby what other users rate to be more influenced by globaldevelopment, while users who follow their own path andrate things in their own bespoke manner would eschew suchglobal information. In prior work of Ver Steeg & Aram theauthors adopted transfer entropy to measure informationtransfer in social media [9]. In doing so the authors wereable to assess for influence in retweeting URLs on Twitterbetween users. Transfer entropy is closely related to Grangercausality, and given two time-series signals, allows one tocompare the e↵ect of one on the other.We adopt transfer entropy to assess how the taste profile

(Ps

) of a user at one time step (s) has been influence bylocal (P

s�1

) and global taste (Qs�1

) profiles at the previouslifecycle stage (s�1). For the latter taste profile (Q

s�1

), weform a global probability distribution as above for a singleuser but instead using all users who posted reviews withinthe time interval of s. From these definitions we can thenexamine the information transfer from a prior lifecycle stage(s� 1) to the current lifecycle stage (s) of the user. Now, as-sume that we have a random variable that describe the localcategories that have been reviewed at the current stage (Y

s

),a random variable of local categories at the previous stage(Y

s�1

). and a third random variable of global categories atthe previous stage (X

s�1

), we then define the transfer en-tropy of one lifecycle stage to another as follows, based onthe work of Schreiber [8]:

TX!Y

= H(Ys

|Ys�1

)�H(Ys

|Ys�1

, Xs�1

) (6)

Using the above probability distributions we can calculatethe transfer entropy based on the joint and conditional prob-ability distributions given the values of the random variables

How much information is transferred from one period to the next?

Decrease = more information is transferred

User properties in period s

User Properties in period s-1

From Mining to Understanding: The Evolution of Social Web Users 14

Evolution measure 3: Transfer Entropy

Pr(c|Du,s

train

) =ave rating(Du,s,c

train

)X

c

02C

u,strain

ave rating(Du,s,c

0

train

)(4)

Based on this formalisation we can assess the relativemean rating score per category for a given user and lifecyclestage. As our item-to-semantic-category mapping function(�) can either map items directly to the categories they areassigned to (�

p

) or to the grandparent categories (�g

) wecan form taste profiles of users using two di↵erent categor-ical levels. Our intuition here was that the former profiletype, formed from directly mapped categories, would leadto sparse profiles due to the greater specificity that the cat-egories denote, while the latter profile type, formed fromtransitively mapped grandparent categories would lead todenser taste profiles. This theory was influenced by the priorwork of Ostuni et al. [6], in which the authors consider onlygrandparent categories aligned to semantic URIs.

5.4 Taste Evolution: Local vs Global Dynam-ics

We now turn to looking at the evolution of users’ tastesover time in order to understand how their preferences change.We are interested in examining for two e↵ects: (i) local dy-namics, the propensity for users to develop in their owninimitable manner; and (ii) global dynamics, where usersexhibit consistent development properties. Given our useof probability distributions to model the lifecycle stage spe-cific taste profile of each user, we apply information theo-retic measures based on entropy judgements capturing: (i)consecutive lifecycle stage development, and (ii) informationtransfer between global taste profiles and the local taste pro-files at one lifecycle stage and the taste profiles of the userat the next stage.

5.4.1 Conditional Category Entropy

By using conditional entropy we can assess the informa-tion needed to describe the taste profile of a user at one timestep (Q) using his taste profile from the previous stage (P ).A reduction in conditional entropy indicates that the user’staste profile is similar to that of his previous stage’s pro-file, while an increase indicates the converse. We define theconditional entropy of two discrete probability distributions,representing taste profiles, as:

H(Q|P ) =X

x2P,

y2Q

p(x, y) logp(x)p(x, y)

(5)

We derived the conditional entropy over the 5 lifecycleperiods in a pairwise fashion, i.e. H(P

2

|P1

), . . . , H(P5

|P4

),and plotted the curve of the mean conditional entropy inFigure 5 over each dataset’s users in the training split, alsoincluding the 95% confidence intervals to show the varia-tion in the conditional entropies. Figure 5 indicates thatMovie Lens users tend to diverge in their ratings and cat-egories over time, given the increase in the mean curve to-wards later portions of the users’ lifecycles, the same is alsoevident for Movie Tweetings, however the increase is moregradual there. Amazon users, however, di↵er by showing areduction in conditional entropy towards later lifecycle peri-ods. Relating this back to our above definition of conditionalentropy, the global e↵ect that we see on Amazon indicates

that users tend to converge in their reviewing behaviour andthat previous profiles allow one to gauge how the user willrate items in the future given their category information.Conversely, for MovieLens and Movie Tweetings we see anopposite e↵ect: users’ taste profiles become less predictableas they develop; users rate items in a way that renders un-certainty in profiling from previous information.

0.22

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0.24

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Cond

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l Ent

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itiona

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(c) Amazon

Figure 5: Parent category conditional entropy be-tween consecutive lifecycle stages (e.g. H(P

2

|P3

))across the datasets, together with the bounds of the95% confidence interval for the derived means.

5.4.2 Transfer Category Entropy

Earlier we postulated that the local development of a userand the global development of all users will have di↵erentinfluential e↵ects on certain users, i.e. influencing how theymay review things. We can examine for such e↵ects underthe premise that local development and global developmentare two di↵erent systems, although the former contributesto the latter we would expect a given user who is influencedby what other users rate to be more influenced by globaldevelopment, while users who follow their own path andrate things in their own bespoke manner would eschew suchglobal information. In prior work of Ver Steeg & Aram theauthors adopted transfer entropy to measure informationtransfer in social media [9]. In doing so the authors wereable to assess for influence in retweeting URLs on Twitterbetween users. Transfer entropy is closely related to Grangercausality, and given two time-series signals, allows one tocompare the e↵ect of one on the other.We adopt transfer entropy to assess how the taste profile

(Ps

) of a user at one time step (s) has been influence bylocal (P

s�1

) and global taste (Qs�1

) profiles at the previouslifecycle stage (s�1). For the latter taste profile (Q

s�1

), weform a global probability distribution as above for a singleuser but instead using all users who posted reviews withinthe time interval of s. From these definitions we can thenexamine the information transfer from a prior lifecycle stage(s� 1) to the current lifecycle stage (s) of the user. Now, as-sume that we have a random variable that describe the localcategories that have been reviewed at the current stage (Y

s

),a random variable of local categories at the previous stage(Y

s�1

). and a third random variable of global categories atthe previous stage (X

s�1

), we then define the transfer en-tropy of one lifecycle stage to another as follows, based onthe work of Schreiber [8]:

TX!Y

= H(Ys

|Ys�1

)�H(Ys

|Ys�1

, Xs�1

) (6)

Using the above probability distributions we can calculatethe transfer entropy based on the joint and conditional prob-ability distributions given the values of the random variablesSurprise in user properties from s-1 to s

Surprise in user properties in s when we consider all users’ properties from s-1

How do global dynamics influence the user’s properties?

Decrease = more susceptible to global influence Increase = less susceptible to global influence

...from Online Communities

Predicting Churners via Evolution Signals 15

From Mining to Understanding: The Evolution of Social Web Users

From Mining to Understanding: The Evolution of Social Web Users 16

examination of user lifecycles we used data collected from Facebook, the SAPCommunity Network (SAP) and Server Fault. Table 1 provides summary statis-tics of the datasets where we only considered users who had posted more than 40times within their lifetime on the platform.1 The Facebook dataset was collectedfrom groups discussing Open University courses, where users talked about theirissues with the courses and guidance on studying. The SAP Community Networkis a community question answering system related to SAP technologies whereusers post questions and provide answers related to technical issues. Similarly,Server Fault is a platform that is part of the Stack Overflow question answeringsite collection2 where users post questions related to server-related issues. Wedivided each platform’s users up into 80%/20% splits for training (and analysis)and testing, using the former in this section to examine user development andthe latter split for our later detection experiments.

Table 1. Statistics of the online community platform datasets.

Platform Time Span Post Count User CountFacebook [18-08-2007,24-01-2013] 118,432 4,745SAP [15-12-2003,20-07-2011] 427,221 32,926Server Fault [01-08-2008,31-03-2011] 234,790 33,285

3.1 Defining Lifecycle Periods

In order to examine how users develop over time we needed some means tosegment a user’s lifetime (i.e. from the first date at which they post to the dateof their final post) into discrete intervals. Prior work [6, 2, 5] has demonstratedthe extent to which users develop at their own pace and thus evolve accordingto their own ‘personal clock ’ [5]. Hence, for deriving the lifecycle periods of userswithin the platforms we adopted an activity-slicing approach that divided auser’s lifetime into 20 discrete time intervals, emulating the approach in [2], butwith an equal proportion of activity within each period. This approach functionsas follows: we derive the set of interval tuples ({[ti, tj ]} 2 T ) by first derivingthe chunk size (i.e. the number of posts in a single period) for each user, we thensort the posts in ascending date order, before deriving the start and end pointsof each interval in an incremental manner. This derives the set of time intervalsT that are specific to a given user.

3.2 Modelling User Properties

Based on the defined lifecycle periods, we now move on to defining user proper-ties, capturing social and lexical dynamics, and tracking how the properties ofusers change over time.

In-degree and Out-degree Distributions. Starting with social dynamics,we assessed the in-degree and out-degree distributions of users: the in-degree

1 Choosing 40 posts so that we had at least 2 posts per lifecycle period.2http://stackoverflow.com/

Datasets: Online Communities

2008 2010 2012

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2004 2006 2008 2010

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s Fr

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2009 2010 2011

050

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Figure 2: Posts per-day for the datasets with thechurner cuto↵s: Facebook = ”2012-07-09”, SAP =”2010-05-11”, and ServerFault = ”2010-12-23”.

we use for evaluating the performance of our predictionmodel described within the following section.

4.1 Historical ComparisonsWe begin by examining the changes that users go through

relative to earlier lifecycle periods, quantified using the cross-entropy between one lifecycle period’s distribution and anearlier lifecycle period that minimises the cross-entropy. Toinform such cross-period assessment we examined the users’in-degree, out-degree and lexical term distributions acrosslifecycle periods by computing the cross-entropy of one prob-ability distribution with respect to another distribution froman lifecycle period, and then selecting the distribution thatminimises cross-entropy. Assuming we have a probabilitydistribution (P ) formed from a given lifecycle period ([t, t0]),and a probability distribution (Q) from an earlier lifecycleperiod, then we define the cross-entropy between the distri-butions as follows:

H(P,Q) = �X

x

p(x) log q(x) (4)

We define a measure as constituting the combination of auser property (e.g. in-degree) assessed along a single devel-opment indicator (e.g. period cross-entropy), thus an exam-ple measure would be in-degree period cross-entropy. We usethese measures to see how the signals of churners and non-churners di↵ers throughout their lifecycles, in essence we areexamining how these di↵erent types of users develop andevolve thereby informing our later churn prediction modelwith predictive cues. The notion of signals is applied as ameans to characterise the development curve, or trajectory,that churners exhibit compared with non-churners over thelifecycle periods.

Figure 3 shows the in-degree, out-degree and lexical pe-riod cross-entopies for Facebook, SAP and Server Fault. Wederived these plots by deriving the measures for each useracross their disparate lifecycle periods, before then derivingthe mean measure for each period for both the churners andnon-churners. We note that across all of the plots churnersignals are lower in magnitude than non-churners signals,indicating that the properties of the non-churners tend tohave a greater divergence with respect to earlier propertiesthan the churners. This suggests that churners’ behaviour ismore formulaic than non-churners, that is they exhibit lessdivergence from what has occurred beforehand. Looking atthe di↵erent user properties in isolation we see that, in gen-eral, the curve of churners and non-churners diminishes to-wards the end of their lifecycles but with di↵erent gradients.

For the in-degree property, churners on Facebook and ServerFault have noticeably flatter curves which reduce at a slowerrate than the non-churners, while for SAP the curves aresimilar for churners and non-churners. For users’ out-degreethe cross-entropy of churners converges on a lower valuemust sooner than non-churners across all platforms; this ef-fect is particularly marked for Server Fault indicating thatnon-churners tend to vary the people with whom they arecommunicating throughout their lifecycles markedly morethan churners. For the cross-entropy of users’ lexical termdistributions we find the signals of churner and non-churnersto follow a similar curvature (converging on a limit with adecaying rate) but with di↵erent magnitudes.

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Figure 3: Period cross-entropy comparing churn-ers with non-churners along: in-degree (Figure 3(a);3(b); and 3(c)), out-degree (Figure 3(d); 3(e); and3(f)) and lexical term distributions (Figure 3(g);3(h); and 3(i)).

4.2 Community ComparisonsFor the second inspection of user lifecycles and how user

properties change, we examined how users compare with theplatform in which they are interacting over the same timeinterval. We used the in-degree, out-degree and lexical termdistributions and compared them with the same distribu-tions derived globally over the same time periods. For theglobal probability distributions we used the same means asfor forming user-specific distributions, but rather than usingthe set of posts that a given user had authored (Pui) to de-

Churner ‘Cutoff’’

From Mining to Understanding: The Evolution of Social Web Users 17

2008 2010 2012

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Figure 2: Posts per-day for the datasets with thechurner cuto↵s: Facebook = ”2012-07-09”, SAP =”2010-05-11”, and ServerFault = ”2010-12-23”.

we use for evaluating the performance of our predictionmodel described within the following section.

4.1 Historical ComparisonsWe begin by examining the changes that users go through

relative to earlier lifecycle periods, quantified using the cross-entropy between one lifecycle period’s distribution and anearlier lifecycle period that minimises the cross-entropy. Toinform such cross-period assessment we examined the users’in-degree, out-degree and lexical term distributions acrosslifecycle periods by computing the cross-entropy of one prob-ability distribution with respect to another distribution froman lifecycle period, and then selecting the distribution thatminimises cross-entropy. Assuming we have a probabilitydistribution (P ) formed from a given lifecycle period ([t, t0]),and a probability distribution (Q) from an earlier lifecycleperiod, then we define the cross-entropy between the distri-butions as follows:

H(P,Q) = �X

x

p(x) log q(x) (4)

We define a measure as constituting the combination of auser property (e.g. in-degree) assessed along a single devel-opment indicator (e.g. period cross-entropy), thus an exam-ple measure would be in-degree period cross-entropy. We usethese measures to see how the signals of churners and non-churners di↵ers throughout their lifecycles, in essence we areexamining how these di↵erent types of users develop andevolve thereby informing our later churn prediction modelwith predictive cues. The notion of signals is applied as ameans to characterise the development curve, or trajectory,that churners exhibit compared with non-churners over thelifecycle periods.

Figure 3 shows the in-degree, out-degree and lexical pe-riod cross-entopies for Facebook, SAP and Server Fault. Wederived these plots by deriving the measures for each useracross their disparate lifecycle periods, before then derivingthe mean measure for each period for both the churners andnon-churners. We note that across all of the plots churnersignals are lower in magnitude than non-churners signals,indicating that the properties of the non-churners tend tohave a greater divergence with respect to earlier propertiesthan the churners. This suggests that churners’ behaviour ismore formulaic than non-churners, that is they exhibit lessdivergence from what has occurred beforehand. Looking atthe di↵erent user properties in isolation we see that, in gen-eral, the curve of churners and non-churners diminishes to-wards the end of their lifecycles but with di↵erent gradients.

For the in-degree property, churners on Facebook and ServerFault have noticeably flatter curves which reduce at a slowerrate than the non-churners, while for SAP the curves aresimilar for churners and non-churners. For users’ out-degreethe cross-entropy of churners converges on a lower valuemust sooner than non-churners across all platforms; this ef-fect is particularly marked for Server Fault indicating thatnon-churners tend to vary the people with whom they arecommunicating throughout their lifecycles markedly morethan churners. For the cross-entropy of users’ lexical termdistributions we find the signals of churner and non-churnersto follow a similar curvature (converging on a limit with adecaying rate) but with di↵erent magnitudes.

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Figure 3: Period cross-entropy comparing churn-ers with non-churners along: in-degree (Figure 3(a);3(b); and 3(c)), out-degree (Figure 3(d); 3(e); and3(f)) and lexical term distributions (Figure 3(g);3(h); and 3(i)).

4.2 Community ComparisonsFor the second inspection of user lifecycles and how user

properties change, we examined how users compare with theplatform in which they are interacting over the same timeinterval. We used the in-degree, out-degree and lexical termdistributions and compared them with the same distribu-tions derived globally over the same time periods. For theglobal probability distributions we used the same means asfor forming user-specific distributions, but rather than usingthe set of posts that a given user had authored (Pui) to de-

Cross-Entropy: dissimilarity with prior in-degree information I.e. how do users who contact a given user differ from before?

From Mining to Understanding: The Evolution of Social Web Users 18

rive the probability distribution, we instead used all posts.For instance, for the global in-degree distribution we usedthe frequencies of received messages for all users. Given thediscrete probability distribution of a user from a time inter-val (P[t,t0]), and the global probability distribution over thesame time interval (Q[t,t0]), we derived the cross-entropy asabove between the distributions. (H(P[t,t0], Q[t,t0])).

Again, as with period cross-entropies, we find churners’signals to have a lower magnitude than non-churners sug-gesting that non-churners’ properties tend to diverge fromthe community as they progress throughout their lifetimewithin the online community platforms. There are some no-ticeably noisy signals however, in particular for Facebookand the in-degree distribution and lexical term distributionsof non-churners. Generally for each signal we see a growingcurve towards later lifecycle periods for both churners andnon-churners, while the magnitudes of the curves are thesalient di↵erentiating feature.

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Figure 4: Community cross-entropy comparingchurners with non-churners along: in-degree (Fig-ure 4(a); 4(b); and 4(c)), out-degree (Figure 4(d);4(e); and 4(f)) and lexical term distributions (Fig-ure 4(g); 3(h); and 4(i)).

5. CHURN PREDICTION MODELOur analysis of the di↵erences between churners and non-

churners exposed latent descriptions and signals of how thesegroups of users develop throughout their lifecycles, findingdi↵erent development signals in terms of each measure’s

magnitude and rate of change. In this section we turn tothe problem of engineering a model to predict churners byusing our prior insights to build features.

5.1 Feature EngineeringOur analysis results indicate that churners and non-churners

di↵ered between one another in terms of: (i) decay ratesfor certain measures, i.e. out-degree period cross-entropy;and (ii) the magnitude of features, i.e. lexical period cross-entropy. Therefore we define two types of features that ourprediction model uses: (i) rates and (ii) magnitudes, whereeach feature is measured for a given lifecycle period. To easefeature definition and model specification, we alter the life-cycle period notation from the existing interval tuple set (i.e.[t, t0] 2 T ) to use a set of discrete single elements: s 2 S,where S = {1, 2, . . . , 20}. Magnitude features are definedas a given user’s measure taken at a given lifecycle period:m(u, s), where the measure for user u is taken at lifecycleperiod s. Rates are defined as changes in measures from onelifecycle period to the next:

�m(u, s) =dm

ds=

m(u, s+ 1)�m(u, s)m(u, s)

(5)

Where �m is indexed by the given measure (i.e. in-degreeperiod cross-entropy), using the above magnitude functionto return the magnitude of a given measure (m) for user uat the allotted lifecycle period. Thus a feature vector (x)is formed for a single user using these rate and magnitudefeatures:

x =[m1(u, 2), . . . ,m1(u, 19),m2(u, 2), . . . ,m2(u, 19), . . .

�m1(u, 2), . . . , �m1(u, 18), �m2(u, 1), . . . , �m2(u, 18)]

As a result of using both rates and magnitudes from eachof the 20 lifecycle periods, aside from the first and last onefor magnitudes and the first and last two for rates, we areprovided with at most 210 features, given the provision of18 magnitude features for each of the 6 measures and 17rate features for each of the 6 measures. As we will de-scribe within the experiments section, we vary the featuresused between di↵erent: (i) feature sets, i.e. in-degree basedfeatures, community cross-entropy based features, etc.; and(ii) lifecycle periods. On this latter aspect we address one ofthe research questions that has driven this work: how earlyinto a user’s lifecycle can we predict them churning? Byconstraining the features to early time periods and thus it-eratively increasing the number of features to use, and hencethe lifecycle periods that the user’s information covers, wedemonstrate the earliest point, for each platform, at whichwe can accurately predict churners.

5.2 Model Definition and LearningWe are provided with, for each of our three online com-

munity platforms, a training dataset and a testing dataseteach taking the following form: {(xi, yi)} 2 D, where xi

defines the feature vector of user ui and yi defines the classlabel of the user, taking a value from the set {0, 1}: 1 ifthe user churned and 0 otherwise. In defining the predic-tion model our goal was to induce a function that predictsthe probability of churning based on a user’s feature vectorf : Rn ! [0, 1]. We define this function as follows for anarbitrary feature vector x and learnt model weights (w) as

Cross-Entropy: dissimilarity with community out-degree information I.e. how do the users that a user contacted differ from the community?

From Mining to Understanding: The Evolution of Social Web Users 19

Predicting Churners

1. Extract Features from Users’ Evolution cross-entropy curves •  Magnitude of the signal @ period s •  Change in the magnitude into from period s to s+1

2. Build the prediction model •  Define the objective function •  Learn the model by minimising the objective:

3. Apply the model •  Over ‘held-out’ data •  Evaluate performance: how accurate is our predictor?

rive the probability distribution, we instead used all posts.For instance, for the global in-degree distribution we usedthe frequencies of received messages for all users. Given thediscrete probability distribution of a user from a time inter-val (P[t,t0]), and the global probability distribution over thesame time interval (Q[t,t0]), we derived the cross-entropy asabove between the distributions. (H(P[t,t0], Q[t,t0])).

Again, as with period cross-entropies, we find churners’signals to have a lower magnitude than non-churners sug-gesting that non-churners’ properties tend to diverge fromthe community as they progress throughout their lifetimewithin the online community platforms. There are some no-ticeably noisy signals however, in particular for Facebookand the in-degree distribution and lexical term distributionsof non-churners. Generally for each signal we see a growingcurve towards later lifecycle periods for both churners andnon-churners, while the magnitudes of the curves are thesalient di↵erentiating feature.

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Figure 4: Community cross-entropy comparingchurners with non-churners along: in-degree (Fig-ure 4(a); 4(b); and 4(c)), out-degree (Figure 4(d);4(e); and 4(f)) and lexical term distributions (Fig-ure 4(g); 3(h); and 4(i)).

5. CHURN PREDICTION MODELOur analysis of the di↵erences between churners and non-

churners exposed latent descriptions and signals of how thesegroups of users develop throughout their lifecycles, findingdi↵erent development signals in terms of each measure’s

magnitude and rate of change. In this section we turn tothe problem of engineering a model to predict churners byusing our prior insights to build features.

5.1 Feature EngineeringOur analysis results indicate that churners and non-churners

di↵ered between one another in terms of: (i) decay ratesfor certain measures, i.e. out-degree period cross-entropy;and (ii) the magnitude of features, i.e. lexical period cross-entropy. Therefore we define two types of features that ourprediction model uses: (i) rates and (ii) magnitudes, whereeach feature is measured for a given lifecycle period. To easefeature definition and model specification, we alter the life-cycle period notation from the existing interval tuple set (i.e.[t, t0] 2 T ) to use a set of discrete single elements: s 2 S,where S = {1, 2, . . . , 20}. Magnitude features are definedas a given user’s measure taken at a given lifecycle period:m(u, s), where the measure for user u is taken at lifecycleperiod s. Rates are defined as changes in measures from onelifecycle period to the next:

�m(u, s) =dm

ds=

m(u, s+ 1)�m(u, s)m(u, s)

(5)

Where �m is indexed by the given measure (i.e. in-degreeperiod cross-entropy), using the above magnitude functionto return the magnitude of a given measure (m) for user uat the allotted lifecycle period. Thus a feature vector (x)is formed for a single user using these rate and magnitudefeatures:

x =[m1(u, 2), . . . ,m1(u, 19),m2(u, 2), . . . ,m2(u, 19), . . .

�m1(u, 2), . . . , �m1(u, 18), �m2(u, 1), . . . , �m2(u, 18)]

As a result of using both rates and magnitudes from eachof the 20 lifecycle periods, aside from the first and last onefor magnitudes and the first and last two for rates, we areprovided with at most 210 features, given the provision of18 magnitude features for each of the 6 measures and 17rate features for each of the 6 measures. As we will de-scribe within the experiments section, we vary the featuresused between di↵erent: (i) feature sets, i.e. in-degree basedfeatures, community cross-entropy based features, etc.; and(ii) lifecycle periods. On this latter aspect we address one ofthe research questions that has driven this work: how earlyinto a user’s lifecycle can we predict them churning? Byconstraining the features to early time periods and thus it-eratively increasing the number of features to use, and hencethe lifecycle periods that the user’s information covers, wedemonstrate the earliest point, for each platform, at whichwe can accurately predict churners.

5.2 Model Definition and LearningWe are provided with, for each of our three online com-

munity platforms, a training dataset and a testing dataseteach taking the following form: {(xi, yi)} 2 D, where xi

defines the feature vector of user ui and yi defines the classlabel of the user, taking a value from the set {0, 1}: 1 ifthe user churned and 0 otherwise. In defining the predic-tion model our goal was to induce a function that predictsthe probability of churning based on a user’s feature vectorf : Rn ! [0, 1]. We define this function as follows for anarbitrary feature vector x and learnt model weights (w) as

the standard linear model: f(x;w) = w|x. We include theL2-regulariser within the model to control for overfitting onthe training splits and test di↵erent �-indexed models. Inlearning the model’s weight vector w, our goal is to minimisethe cost function (C(w)) with respect to the weight vector:

C(w) =1

2|Dtrain|

X

i=1

(f(xi;w)� yi)2 + �kwk22

!(6)

Where the latter term (kwk2) defines the L2-regularizerand � defines the weight of the regularizer’s e↵ect on themodel, and thus controls for overfitting on the training split:

kwk22 =⇣ |w|X

j=0

|wj |2⌘ 1

2(7)

For learning the parameter weight vector (w) we use gra-dient descent by learning from instances within each trainingsplit. Algorithm 2 summarises the model learning proce-dure.4 We iteratively learn the weight vector, in the outerloop, until either the maximum number of training epochshas been reached or the weight vector has converged on somelimit (✏). Learning is performed over each parameter in theweight vector (line 6) using the update rule (line 7) to up-date the the weight vector based on the loss of the parameterover all samples, and the regularizer.

Algorithm 2 Learning the weight parameter vector (w)using gradient descent. Input: ⌘, ✏, Dtrain. Output: w

1: w random(n)2: w random(n)3: e 04: while (e < max e) && (||w �w|| � ✏) do5: w w6: for j 2 {0, 1, . . . , |w|} do7: wj = wj � ⌘

�1m

Pmi=1(f(x

i;w)� yi)xij +

�mwj

�

8: end for9: e e+ 110: end while11: return w

To examine the e↵ect of learning on the model’s perfor-mance, we use the above cost function based on the lossin predictions made over the training samples. As we aredealing with a binary class label and real-valued continu-ous feature vector as input, we want the co-domain of thelearnt function to be a reduced probability if the underly-ing class label is 0 and an increased probability if the classlabel is 1, thus reducing the associated cost of the function.As we iteratively learn the model parameters we should seeconvergence of the cost function on a stable setting. Thefree parameters in our model are: (i) the learning rate (⌘),which controls the rate at which the model’s weight vectoris updated; and (ii) the regularisation weight (�). We testdi↵erent settings of � when predicting churners in order toassess the e↵ect that regularisation has on predictive perfor-mance, and tune the learning rate ⌘ and weight vector w fordi↵erent settings of �. Hence we run the learning processfor di↵erent settings of ⌘ and �, reporting on the convergedmodel’s cost as a result.4We use R scripts to run the learning process. These will beprovided in a Github repository for the camera-ready versionof the paper, should it be accepted.

6. EXPERIMENTSIn this section we describe our churn prediction experi-

ments across the three datasets. We begin by explainingthe experiments conducted and their setup, before then pre-senting our results and how well we fare against existingwork.

6.1 Experimental SetupFor our experiments we prepared the training and testing

splits as mentioned above (i.e. deriving features per userin each platform’s splits), and then standardised each fea-ture to have unit variance (µ = 0,� = 1). We ran threeexperimental procedures: we set the regularisation weightto five discrete values � = {0, 1, 2, 5, 10} to assess the e↵ectthat regularisation has on predicting churners, and tunedthe learning rate (⌘) and the model’s weight vector (w) foreach setting of � and the three online community platforms.We set the convergence threshold between training epochs tobe ✏ = 0.0001 and the maximum number of training epochsto be 1000. We recorded the final cost of each model overthe training splits, and identified the learning rate that min-imised the cost together with the weight vector. This firstexperiment formed the model tuning stage. For our secondexperiment, we used used the weight vector (w) tuned foreach value of � to predict churners using di↵erent featuresets. For di↵erent feature sets we examined the achievedperformance and how this di↵ered between the platformsand features applied. For the third experiment, we took thebest performing model, based on feature set selection, anditeratively added features from the earliest lifecycle periodsto the latest, thus examining how early into a user’s lifecyclewe can accurately predict them churning.

6.1.1 Evaluation MeasureTo evaluate the accuracy of the induced models, both for

our aforementioned linear model and the baselines that aredescribed below, we used the Area Under the receiver char-acteristic Curve (AUC), a metric which is widely used withinchurn prediction literature. To derive the area under the re-ceiver operator characteristic curve we varied the confidenceof an indicator function (I(x)) through discrete settings ofconfidence bounds ✓ = {0, 0.05, . . . , 0.95, 0.1}, thereby set-ting the class label for given instance (x) as follows:

I(x) =

⇢1, if Pr(Y = 1 | xi) > ✓ (8a)

0, otherwise (8b)

For each di↵erent setting of ✓ we measured the true pos-itive rate (TPR/recall) and the false positive rate (FPR),and from these measures plotted the receiver operator char-acteristic (ROC) curve. A model which maximises the areaunder this curve (AUC) is preferable (thus achieving a valueof 1), where the baseline for this measure is 0.5.

6.1.2 BaselinesWe deploy two baselines for our experiments, the first is

an implicit baseline within the AUC measure of 0.5 suchthat a diagonal line intersects the ROC space, which ourprediction model aims to surpass; the second explicit base-line is based on state of the art work by Karnstedt et al., [5].In [5] the authors developed a model for predicting churnersfrom the online community message board Boards.ie5 which

5http://www.boards.ie

Error of the model

Goal: learn w by reducing this

From Mining to Understanding: The Evolution of Social Web Users 20

Evaluation: Results Table 3: Area Under the receiver operator characteristic Curve (AUC) scores for the di↵erent regularisedprediction models and the J48 baseline model from the state of the art (denoted by J48). Best model perplatform is in bold and significance of improvement over the random model baseline is indicated.

Platform Feature Set � = 0 � = 1 � = 2 � = 5 � = 10Facebook In-degree 0.535. 0.543. 0.538. 0.556* 0.549** J48 = 0.586 Out-degree 0.674*** 0.666*** 0.676*** 0.696*** 0.690***

Lexical 0.633*** 0.630*** 0639*** 0.637*** 0.641***Cross-period 0.649*** 0.642*** 0.649*** 0.652*** 0.651***Cross-community 0.684*** 0.693*** 0.691*** 0.699*** 0.701***All 0.811*** 0.804*** 0.816*** 0.817*** 0.819***

SAP In-degree 0.652*** 0.651*** 0.651*** 0.652*** 0.654*** J48 = 0.759 Out-degree 0.741*** 0.742*** 0.742*** 0.742*** 0.743***

Lexical 0.501 0.501 0.501 0.499 0.497Cross-period 0.614*** 0.614*** 0.614*** 0.613*** 0.612***Cross-community 0.765*** 0.765*** 0.765*** 0.765*** 0.765***All 0.816*** 0.817*** 0.817*** 0.817*** 0.818***

Server Fault In-degree 0.659*** 0.658*** 0.662*** 0.663*** 0.663*** J48 = 0.796 Out-degree 0.618*** 0.617*** 0.616*** 0.619*** 0.626***

Lexical 0.680*** 0.682*** 0.687*** 0.686*** 0.684***Cross-period 0.671*** 0.675*** 0.680*** 0.691*** 0.689***Cross-community 0.778*** 0.779*** 0.780*** 0.778*** 0.779***All 0.858*** 0.860*** 0.861*** 0.861*** 0.860***

Significance codes: p-value < 0.001 *** 0.01 ** 0.05 * 0.1 . 1

cycle periods to late lifecycle periods. Across all three plat-forms we find that performance improves as additional in-formation is added into the models. There are di↵erences,however, in the gradient in performance between the plat-forms, indicating the added e↵ect of certain lifecycle periodsover others. For instance, for Facebook and Server Fault,the rate of performance gain is relatively linear, with somefluctuation for the latter platform; this suggests that infor-mation to predict churners is relatively evenly spread acrossthe lifecycle periods of the users. For SAP we see a slightlydi↵erent performance growth curve: there is a large boostin performance as earlier lifecycle period features are added,followed by a gradual increase in performance, that also ap-pears linear, following the 4th and 5th lifecycle periods. Thissuggests that for SAP, one can use relatively early develop-ment signals to predict who will churn from who will not.Indeed, the AUC value of ⇠ 0.7 achieved from including allfeatures up to and including the 4th lifecycle period suggeststhat the induced model has a 70% chance of correctly dif-ferentiating a churner from a non-churner. With Facebook,however, that level of performance is achieved once the 12thlifecycle period’s features are included.

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0 5 10 15 20

0.5

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0.7

0.8

0.9

Lifecycle Period

AUC

(a) Facebook

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0 5 10 15 20

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Lifecycle Period

AUC

(b) SAP

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0 5 10 15 20

0.5

0.6

0.7

0.8

0.9

Lifecycle Period

AUC

(c) Server Fault

Figure 6: Area Under the receiver operator char-acteristic Curve (AUC) values based on iterativelyadding lifecycle period features.

7. DISCUSSION AND FUTURE WORK

Our churn prediction approach makes use of the develop-ment signals that users exhibit along both social and lexicaldimensions in order to di↵erentiate between who will churnand who will remain within the online community platform.In comparison with the work of Kernstadt et al. [5], we usedynamic user information, that is: information about howthe user has evolved throughout his lifecycle to date, whileKernstadt et al. adopt static user information derived usinga 6-month window prior to a given analysis point. A limi-tation of our approach, however, is the reliance on knowingthese lifecycle periods a priori, as, without this knowledge,one could not derive a given measure for a particular userrelative to their earlier behaviour. Therefore a natural pro-gression of this work for the future is to investigate adapt-ing the approach to predict churners given an arbitrary timepoint. Prior work of Danescu et al. [2] examined the e↵ectof lexical features on churn prediction and found that theincorporation of term cross-entropy, derived by comparinga user’s term distribution with that of the community froma window of 12-months either side of a given lifecycle pe-riod, improved prediction performance. Our incorporationof cross-community features, across both social and lexicaldimensions, into the prediction model consistently achievesimproved performance over the use of solely lexical features.This suggests that although lexical information describinguser development aids churn prediction, social developmentsignals contain added information; although the benefits ofsocial information vary between the online community plat-forms - for instance when comparing Facebook and SAPwith ServerFault lexical features outperform the social fea-tures on the latter platform.For inducing our linear prediction model we chose to adopt

gradient descent rather than stochastic gradient descent.Our future work will explore the e↵ect that per-user learn-ing can have on model induction and parameter learning.Another alteration that we plan to make to our model inthe future is to alter the discrete settings of the learningrates (⌘) per �-indexed regularised model in favour of de-creasing learning rates. Such adaptive learning rates havebeen pointed out in the work of Streeter & McMahan [15]

=State of the art baseline

Higher = better Min = 0, Max = 1!

From Mining to Understanding: The Evolution of Social Web Users 21

By mining users’ evolution signals we can accurately predict who will churn, and who will not…

…this enables the early application of retention strategies

Recommending Items from Taste Evolution 22

From Mining to Understanding: The Evolution of Social Web Users

Recommender Systems aim to either: (i)  Predict item adoptions

(ii)  Predict item ratings

from Ys

, Ys�1

and Xs�1

:

TX!Y

=X

y2Ys,

y

02Ys�1,

x2Xs�1

p(y, y0, x) logp(y|y0, x)p(y|y0)

(7)

We derived the transfer entropy between consecutive life-cycle periods, as with the conditional entropy above, to ex-amine how the influence of global and local dynamics onusers’ taste profiles developed over time. Figure 6 plots themeans of these values across the lifecycle periods togetherwith the 95% confidence intervals. We find that users ofMovieLens transfer entropy decrease over time, indicatingthat global dynamics have a stronger influence on users’taste profiles towards later lifecycle stages. Such an e↵ect ischaracteristic of users becoming more involved and familiarwith the review system, and as a consequence paying atten-tion to more information from the users. With Movie Tweet-ings and Amazon we find a di↵erent e↵ect: users’ transferentropy actually increases over time, indicating that usersare less influenced by global taste preferences, and thereforethe ratings of other users, and instead concentrate on theirown tastes.

0.12

00.

122

0.12

4

Lifecycle Stages

Tran

sfer

Ent

ropy ●

●

●

●

1 2 3 4 5

(a) Lens

0.11

20.

114

0.11

6

Lifecycle Stages

Tran

sfer

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ropy

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1 2 3 4 5

(b) Tweetings

0.13

00.

132

0.13

40.

136

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(c) Amazon

Figure 6: Parent category transfer entropy betweenconsecutive lifecycle stages (e.g. H(P

2

|P3

)) across thedatasets, together with the bounds of the 95% con-fidence interval for the derived means.

6. RECOMMENDATIONSFindings from the previous section indicate a link be-

tween lifecycle duration and taste evolution across the plat-form: -Entropy: users’ tastes profile reduce in variation onMovieLens, reduce then go up on Tweetings, and increasethen decrease on Amazon -Conditional Entropy: Lens andTweetings show that users diverge in their tastes consecu-tively, while Amazon users converge -Transfer Entropy: Lensusers are more strongly influenced by global tastes over time,while Tweetings users are less influenced by global tastesover time, while Amazon...

Hence time has a strong e↵ect on the taste profile of theuser and the likelihood of him rating an item from a givencategory positively

6.1 Recommendation Model FormulationWe use the following model for our recommender system

based upon matrix factorisation:

rui

= bui

+ p|u

qi

(8)

6.2 BiasesThe biases in our model are defined as follows:

bui

=

Staticz }| {µ+ b

i

+ bu

+

Evolvingz }| {bi,cats(i)

+ bu,cats(i)

(9)

6.2.1 Static Biases

The bias component of our model contains static biases in-duced from the training segment. There include the generalbias of the given dataset (µ), which is shown in Figure 7 asthe mean rating score across all ratings within the trainingsegment. The use of the mean on its own is insu�cient - i.e.note the variance in ratings scores for the Amazon Moviesdataset - therefore we also include the item bias (b

i

) andthe user bias (b

u

). The former bias is the average deviationfrom the mean bias for the item i within the training seg-ment, while the latter bias is the average deviation from themean bias from the training segment’s ratings by user u.

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p(x)

1 2 3 4 5

10−4

10−3

10−2 µ=3.7

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p(x)

1 2 3 4 5 6 7 8 9

10−5

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100

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Lifetime (in days) per user

p(x)

1 2 3 4 5

10−8

10−6

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100

µ=4.1

(c) Amazon

Figure 7: Distribution of users’ ratings across thethree datasets

6.2.2 Category Biases

Item Biases Towards Categories.

Item bias given the categories-Evolution of the category biases in the training segment,

anticipated evolution into the test segment -Using globaltaste profiles to work this outWant to capture the proportional change in category rat-

ings across the entire platform, to do this we derive thedevelopment of all users’ preference for a given category cthroughout the training segment, where Q

s

is the globaltaste profile (discrete probability distribution of all cate-gories):

�c

=1

4� k

4X

s=k

Qs+1

(c)�Qs

(c)Q

s

(c)(10)

From this we can then calculate the conditional probabil-ity of a given category being rated highly within the testsegment by accounting for the change rate of rating prefer-ence for the category as follows:

Pr(+|c) =Prior Ratingz }| {Q

5

(c) +

Change Ratez }| {�

c

Q5

(c) (11)

Thereby, by averaging this over all categories for the itemi can can calculate the evolving item bias from the trainingsegment:

bi,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c) (12)

From Mining to Understanding: The Evolution of Social Web Users 25

Table 1: Statistics review datasets used for our analysis and experimentsDataset #Users #Items #Ratings Time Span Ratings ScaleMovieLens 6,024 3,678 902,585 [26-04-2000,31-12-2000] [1,5]Movie Tweetings 19,043 11,451 117,206 [28-02-2013,23-09-2013] [1,10]Amazon Movies & TV Reviews 889,173 253,059 7,880,387 [20-08-1997,25-10-2012] [0,5]Total 914,240 268,188 8,900,178 - -

coverage.

4.2 Amazon MoviesFor the Amazon Movie and TV Reviews dataset we were

provided with Amazon Standard Identification Numbers (ASINs)as identifiers of items. We looked up the ASINs for each itemin the dataset by querying the Amazon Product AdvertisingAPI2 and returning the item information including: title, ac-tors, and directors. Unlike MovieLens and Movie Tweetings,we were not provided within the year of release informationfrom the API, therefore to perform the disambiguation of se-mantic URIs we used the actor information from each movie:our intuition being that each movie would have a unique setof actors starring in it. Therefore we stored the actors associ-ated within each item as additional background informationand performed disambiguation in a similar vein as above:we first identified candidate URIs for a given movie itemby performing fuzzy matches between the item title and se-mantic URIs’ titles. We then derived the correct URI bycomparing the set of actors associated with the item (A

a

)and the set of actors associated within each candidate URI(A

c

), selecting the candidate URI based on maximising theset overlap: argmax

c2C

|Ac

\Aa

|Figure 4.2 presents how our running example the film

‘Alien’ is aligned from the Amazon Movies Dataset to itssemantic URI within the linked data cloud. The title ismatched with the rdfs:label of the semantic URI, follow-ing which the movie item’s actors ‘Sigourney Weaver ’, and‘John Hurt ’ are matched with instances of foaf:Person viathe foaf:name property. Using this approach we achieve amuch lower coverage rate than the MovieLens and Movi-eTweetings datasets of 9%.

dbpedia:Alien_(film)

dbpedia-owl:Film

dbpedia:Sigourney_Weaver

foaf:Person"Sigourney Weaver"

rdf:type

rdf:typefoaf:name

dbprop:starring

dbpedia:John_Hurt

"John Hurt"

dbprop:starring

rdf:type foaf:nameItemID ActorB00004S8GO Sigourney WeaverB00004S8GO John Hurt

ItemActors

ItemID TitleB00004S8GO Alien

Items

"Alien"rdfs:labelAmazon Movies Dataset

Figure 1: Graph-based disambiguation of Amazonmovies via actor links.

4.3 Reduced Datasets and the Hipster DilemmaBased on our alignment of the movie items within each re-

spective dataset with their semantic URIs within the linkeddata cloud we derived new datasets. As one would expect,2http://docs.aws.amazon.com/AWSECommerceService/latest/DG/CHAP_Intro_AAWS.html

the statistics of these datasets shown in Table 2 demon-strates the extent to which the items, users and ratings havebeen reduced. Figure 2 presents the distribution of reviewsper users within each of the reduced datasets; we note thatthe collection strategy of MovieLens (concentrating on userswho have reviewed more than 20 items) skews the distribu-tion towards users who have produced many reviews, whilefor Movie Tweetings and the Amazon datatsets we see heavytailed distributions. Table 2 also indicates that there is alarge reduction in both users and items overall, however thereduction in the number of ratings is not as great, this sug-gests two things: (i) mapped items are popular, and thusdominate the ratings; and (iii) obscure items are presentwithin the data. In particular for the Amazon dataset , de-spite our alignment covering only 10.6% of items we onlyhave a reduction of 26.9% of the total ratings, suggestingthat we cover the ‘head ’ of the ratings distribution in termsof popularity.

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Reviews per User

p(x)

100 101 102 10310−4

10−3

10−2 µ=139.7

(a) Lens

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Reviews per User

p(x)

101 102 103 10410−8

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100

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Figure 2: Distribution of reviews per user across thethree datasets

The resulting alignment of items with semantic URIs, andthe coverage achieved, leads one to wonder: why do we man-age to map certain movies and not others? As Table 2 sug-gests, certain more ‘obscure’ movies do not have URIs withinthe linked data cloud, and despite our use of the most recentDBPedia datasets (i.e. version 3.9) coverage is still limitedin certain places. The reason for this lack of coverage forcertain items is largely due to the obscurity of the film nothaving a wikipedia page. For instance, for the MovieLensdataset we fail to map the three movies ‘Never Met Picasso’,‘Diebinnen’ and ‘Follow the Bitch’, despite these films hav-ing IMDB pages they have no wikipedia page, and henceno DBPedia entry. For the Movie Tweetings dataset wefail to map ‘Summer Coda’ and ‘The Potted Psalm’, bothof which, again, have IMDB pages but no wikipedia page.We also note that for several foreign language films whosetitles are in their native language we fail to achieve a map-ping (e.g. ‘La horse’) given our restriction of English titleswithin the SPARQL query above. For Amazon, we excludedmany items from the outset by only concentrating on movies,while the Amazon dataset contains both movies and televi-

Recommendation Datasets: Item-Ratings

5.2 Datasets SplittingOne of the aims of our work is to engineer a recommender

system that accounts for the development of users’ tastesover time. We therefore need to be able to test this systemin a setting which assesses its generalisation capability - i.e.its ability to perform ‘well ’ over unseen data. To enablethis we divided each of our three platforms’ datasets up intoa training and a testing segment. We ordered each ratingby the time at which it was created and maintained the first80% as the training set, and the latter 20% as the testing set.Figure 4 presents the cuto↵ points for each dataset: 10-11-2000 for MovieLens, 12-08-2013 for Movie Tweetings, and12-10-2009 for Amazon. We used the training to performthe analyses described within this section and to induce ourlater recommendation system.

May Jul Sep Nov JanTime

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ber o

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iew

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Figure 4: Distribution of reviews per day across thethree datasets

5.3 Taste ProfilesTaste profiles describe the preferences that a user has at

a given point in time. We are interested in understandinghow a profile at one point in time compares to a profile at anearlier point in time, in essence observing whether taste evo-lution has taken place, or not. In recent work by McAuleyand Leskovec [5] the assessment of user-specific evolutionin the context of review platforms (e.g. BeerAdvocate andBeer Review) demonstrated the propensity of users to evolvebased on their own ‘personal clock ’. This means that if weare to segment a user’s lifetime on the system into discretelifecycle periods where each period is the same width in time,then we will have certain periods with no activity in them:as the user may go away from the system duration the mid-point of their lifetime, and then return later.

To counter this we divide user’s lifecycle into 5 stageswhere each stage contains the same number of reviews, wedenote this as ‘activity-based lifecycle slicing ’. This processis described within Algorithm 1: we begin by defining thechunk size for a given user based on his reviews within thetraining split (line 1), we then sort the users reviews in as-cending time order (line 2). We then form the 5 lifecycleperiods by deriving the start and end review indices for theposts within the given stage (lines 6 and 7), before then de-riving the time at which these reviews were posted, therebygiving the start and end bounds for the given stage (lines11 and 12). The stage is then recorded as a pair and storedwithin the set of tuples (T ), these are then returned.

One of the issues that we encountered when modellingusers’ lifecycle stages was the fidelity of the stages. Priorwork has used 20 lifecycles periods [7, 5] to model user de-velopment, however we found this number to be too high:a key restriction of forming taste profiles is that one needs

Algorithm 1 Deriving the set of lifecycle stages (T )

1: chunkSize |Dutrain|/5

2: Qu sort(Dutrain)

3: i 04: T ;5: while i < 5 do

6: start i⇥ chunkSize

7: end (i + 1)⇥ chunkSize

8: if end > |Qu|� 1 then

9: end = |Qu|� 110: end if

11: ti time(Qu[start])12: tj time(Qu[end])13: T T [ {[ti, tj ]}14: end while

15: return T

su�cient information from which to mine them, hence alarger number of lifecycle periods would needs more reviewsfor each user. We used the restriction imposed in Rowe’swork [7] of 2 reviews per stage, thus requiring at least 10reviews per person overall, rather than 40 should we haveused 20 lifecycle periods. This increases the number of usersfor whom we can assess taste evolution throughout theirlifecycle stages. For the analysis of users within the train-ing segment, and the development of their tastes through-out their lifecycle stages, we have 3,406 (56%) of users forMovieLens, 2,065 (11.5%) of users for Movie Tweetings and83,498 (18.7%) of users for Amazon. The low coverage thatwe achieve here is due to the number of reviews that we needto form the lifecycle stages from, we explain in the followingsection how our recommendation system accounts for thoseusers whose taste development cannot be mined.

5.3.1 Forming Taste Profiles

In order to form taste profiles we formalise the ratingsdistribution per category for a given user based on theirreviews within an allotted time window, provided by thelifecycle stage of the user. To aid legibility we use the integerset of lifecycle periods (Z⇤

6

) which are mapped, via an ontoand one-one function f , to the set of lifecycle stage tuples(f : S ! T ). We form a discrete probability distribution forcategory c at time period s by interpolating the user’s ratingswithin the distribution. Rather than merely counting thenumber of items within a particular category that have beenreviewed, we instead include the ratings when calculatingthe distribution. We first define two sets, the former (Du,s,c

train

)corresponding to the ratings by u during interval s for itemsfrom category c, and the latter (Du,s

train

) corresponding toratings by u during s, hence Du,s,c

train

✓ Du,s

train

, these sets areformed as follows:

Du,s,c

train

= {(u, i, r, t) : (u, i, r, t) 2 Dtrain

, t 2 s, c 2 �(i)}(1)

Du,s

train

= {(u, i, r, t) : (u, i, r, t) 2 Dtrain

, t 2 s} (2)

We then define the function ave rating to derive the av-erage rating value from all rating quadruples in the givenset:

ave rating(Du,s

train

) =1

|Du,s

train

|X

(u,i,r,t)2D

u,strain

r (3)

From these definitions we then derive the discrete proba-bility distribution of the user’s ratings per category as fol-lows, defining the set Cu,s

train

as containing all unique cate-gories of items rated by u in stage s:

User u…

…rated item i…

…with score r…

…at time t

From Mining to Understanding: The Evolution of Social Web Users 26

Forming Taste Profiles

s Item Rating

Alien 4*

Bladerunner 5*

Star Wars 4*

3. DATASETSMovieLens: using 1m dataset -Stripped out the movies

which appeared after 2000, due to sparsity in the reviewcount per day - this trailed o↵ -Resulted in a reduction of95 days as the mean lifetime per user to 12 days, thus in-dicating that some users stayed on as ’committed’ users tothe platform

Movie Tweetings: -From the CrowdRec workshopAmazon Movie Reviews: using SNAP dataetDataset processing: -Split each dataset up into a training

and testing split using a time-sensitive split where the first80% of days contained the training data and the later 20%contained the test data

Linked Data Datasets used: DBPedia 3.9

4. DISAMBIGUATION OF SEMANTIC URISFOR MOVIE ITEMS

Assessing the evolution of users’ tastes involves inspect-ing the changing preferences of users over time, characteris-ing such preferences through categorical information aboutrated items (e.g. “romantic comedies”, “film noir”, etc.).Linked data provides an ideal resource for such informa-tion, where movies appear within the linked data cloud asUniform Resource Identifiers (URIs) which, upon derefer-encing, return information about the movie: director, yearof release, actors, distributor, etc. Additionally, movies areplaced within categories denoting their genre and subjectmatter, these categories can, in turn, be derefenced and theirinformation returned. For instance, for the movie ‘Alien’ re-leased in 1970, which we shall now use as a running example,the following categories are found:

<http :// dbpedia . org / r e sou r c e / A l i en ( f i lm )>dcterms : sub j e c t category : A l i en ( f r a n ch i s e ) f i lm s ;dcterms : sub j e c t category :1979 h o r r o r f i lm s ;dcterms : sub j e c t category : Space adventure f i lms ;dcterms : sub j e c t category : F i lm s s e t i n t h e f u t u r e .

Subject categories form a hierarchical structure such thatparent categories define more general subjects. For instancethe category category:Films_set_in_the_future is linkedto category:Science_fiction_films_by_genre by the pred-icate skos:broader, thus providing a general taxonomic clas-sification of the film. The advantage of such a structure isthat we can explicitly identify a given user’s tastes at a givenpoint in time via the categories of films that they have con-sumed, and thus rated. In order to provide such information,however, we require a link between a given item within oneof our three datasets and the semantic URI that denotesthat movie item. However in deriving semantic web URIsfor films we may encounter ambiguity issues where multiplefilms share the same title - this often happens with film re-makes. Therefore we use available information from each ofour datasets to disambiguate the semantic URIs and thusreturn the correct alignment. In this section we describethis disambiguation procedure across the three datasets us-ing two methods: one based on title and year of the movieitems, for MovieLens and Movie Tweetings; and a secondmethod based on the title and actor information, for Ama-zon Movie Reviews.1

1Should the paper be accepted for publication, we shall in-clude the mapping files between items (from the recommen-dation datasets) and semantic URIs in the linked data cloud.

4.1 MovieLens and Movie TweetingsFor the MovieLens and Movie Tweetings datasets we are

provided with item records that contain the item’s title andyear (release year of the movie). Our method for semanticURI disambiguation functioned as follows: first, we used thequery from [6] to extract all films (instances of dbpedia-

owl:Film) from DBPedia which contained a year within oneof their categories:

SELECT DISTINCT ?movie ? t i t l e WHERE {?movie rd f : type dbpedia�owl : Film ;

r d f s : l a b e l ? t i t l e ;dcterms : sub j e c t ? cat .

? cat r d f s : l a b e l ? year .FILTER langMatches ( lang (? t i t l e ) , ”EN”) .FILTER regex (? year , ”ˆ[0�9]{4} f i lm ” , ” i ”)

}

Using the extracted mapping between the movie URI (?movie)and title (?title) we then identified the set of candidateURIs (C) based on performing fuzzy matches between agiven item’s title and the extracted title from DBPedia.Fuzzy matches were performed using the Levenshtein sim-ilarity metric (derived from the normalised reciprocal Lev-enshtein distance) and setting the similarity threshold to0.9. We use fuzzy matches here due to the di↵erent formsof the movie titles and abbreviations within the datasetsand linked data labels. After deriving the set of candidateURIs, we then dereferenced each URI and looked up itsyear to see if it appears within an associated category (i.e.?movie dcterms:subject ?category). If the year of themovie item appears within a mapped category (?category)then we identified the given semantic URI as denoting theitem.We tried variations of this approach before converging on

the above method and assessed the performance of eachbased on the coverage of the mappings: that is, the pro-portion of items within each of the respective datasets thatare aligned with a URI. We found that by directly matchingthe title (i.e. strict syntactic match) we achieved coverage of71% for MovieLens, and 57% for Movie Tweetings. By us-ing the foaf:name property to return the name of the moviefrom its semantic URI and then perform a fuzzy match be-tween the titles to return the candidate set, we achievedcoverage of 75% and 60% for MovieLens and Movie Tweet-ings respectively. However by using the rdfs:label property,and thus returning a list of alternative labels for the moviefrom its semantic URI, and then performing a fuzzy matchbetween the titles, we achieved coverage of 83% and 69% forMovieLens and Movie Tweetings respectively.It is worth noting that we also tried another approach for

the Movie Tweetings dataset: as the datatset was derivedfrom Tweets containing IMDB links, it was possible to usethe IMBD item numbers to look up the movie items withinthe linked data cloud. One repository for this was the LinkedMovie Database (LinkedMDB), however due to the MovieTweetings dataset being collected relatively recently (last re-view was in 25-10-2013) there were many movies which werenot found within the LinkedMDB. We postulate that thisis due to the behaviour that users exhibit when reviewingmovies on IMDB and through their app: upon completinga review it is possible to share the review on Twitter. Usersmay be doing this following the viewing of a movie withinthe cinema, and given the recent dates that the dataset cov-ers this leads to a mismatch between the LinkedMDB reposi-tory and the recommendations dataset, thus producing poor

Table 2: Statistics of the revised review datasets used for our analysis and experiments. Reduction over theoriginal datasets are shown in parentheses.

Dataset #Users #Items #RatingsMovieLens 6,024 (-0%) 3,231 (-12.1%) 841,602 (-6.7%)Movie Tweetings 17,827 (-6.3%) 7,913 (-30.8%) 104,055 (-11.2%)Amazon 444,861 (-49.9%) 27,066 (-89.4%) 5,564,199 (-29.3%)Total 468,712 (-48.7%) 38,210 (-85.7%) 6,509,856 (-26.9%)

sion programmes. Again, we find that obscure films such as‘Cry of the Black Wolves’ was not aligned to a semantic URIdespite it having a IMDB page. We define the challenge ofaddressing the obscurity of movies, and thus their lack of aDBPedia entry, as the hipster dilemma. In the discussionssection of the paper we outline several strategies for deal-ing with this in the future given its presence not only inthis work but in the prior work of Ostuni et al. [6], and itpotential e↵ect on future work within this domain.

4.3.1 Category Ratings

To provide a first look into to the link between seman-tic categories and ratings, we examined the average ratingsof the top-2 most frequently reviewed categories across thedatasets. This was derived by recording the frequency ofcategories linked to by rated items within the training split,and then selecting the top-2 most frequent. In Figure 3 weplotted the development of the average rating score acrossthese two categories, derived using a 7-day moving averageto smooth the variance in rating fluctuations. We find thatthere are peaks and troughs in the reviewing of the itemsthat belong to the categories, in particular one can note thatfor MovieLens the scores remain relatively stable, while forMovie Tweetings ‘Independent Films’ reduce in their averagerating and ‘Directorial Debut films’ increase in their averagerating over time. Such information can be encoded withinthe biases of the recommendation models and consider thestability of a given bias in light of when the rating is beingmade: i.e. considering the fluctuation of the rating signaland how this relates to previous fluctuations.

May Jul Sep Nov

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age

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age

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Figure 3: Average ratings derived using a 7-daymoving average of the top-2 most frequently ratedcategories.

5. ANALYSING TASTE EVOLUTIONAnalysing the evolution and development of users’ tastes

allows one to understand how a given user is likely to ratea given item in the future. In the context of this paper we

concentrate on movie items; this domain is unique for en-compassing a variety of genres, where movies can be placedin categories (as described above). We are interested in try-ing to understand three things: (i) global evolution dynam-ics, describing how users in general transition and developin their preferences over time; (ii) local evolution dynamics,in terms of how a specific user is evolving his tastes; andfinally (iii) the association between global and local dynam-ics. This latter aspect concerns the influence that generaltrends of taste evolution have on a given user: we postulatethat certain users will be more greatly influenced by suchdynamics than others, and this is something that we controlfor in our recommendation model which follows this section.In this section we analyse for global and local dynamics, andmine the relation between local and global dynamics in in-fluencing users’ tastes. In particular, given our use of threedi↵erent datasets derived from three distinct sources, we areinterested in understanding how local and global taste evo-lution di↵ers, and the influence that one has on the otherfor the platforms’ users.

5.1 Preamble: NotationFrom this point onwards we are entering the realm of rec-

ommender systems, and therefore to aid comprehension andease of legibility we reserve the following special charactersfor set notations, as follows:

• u, v denote users• i, j denote items• r denotes a known rating value (where r 2 R), and r

denotes a predicted rating value• Datasets are provided as quadruples of the form (u, i, r, t) 2

D and are segmented into training (Dtrain

) and testing(D

test

) datasets by the above mentioned cuto↵ pointssuch that D

train

\Dtest

= ;• c, c0 denote category concepts within the linked data

graph and C denotes the set of categories. The graphitself is denoted by: G = hC,Ei, where e

c,c

0 2 E de-notes the set of edges, or concept relations, that con-nect concepts together within the graph. We use a di-rected graph and only consider hierarchical relations:i.e. e

c,c

0 denotes the edge connecting c and c0 throughthe triple c skos:broader c0 such that c has a broader,and thus more general category, denoted by c0.

• � denotes a mapping function between items and se-mantic categories, realised through the disambigua-tion of semantic URIs for items. The mapping func-tion either maps items to their direct parent cate-gories: �

p

: I⇥C;3 or maps items to their transitively-connected grandparent categories: �

g

: I ⇥ C.4

3I.e. Using the statement: i dcterms:subject c4I.e. Via: i dcterms:subject ?p, ?p skos:broader c

Item Rating

Space_adventure (4+4)/2 = 4

Science Fiction (4+5+4)/3 = 4.3

Pr(c|Du,s

train

) =ave rating(Du,s,c

train

)X

c

02C

u,strain

ave rating(Du,s,c

0

train

)(4)

Based on this formalisation we can assess the relativemean rating score per category for a given user and lifecyclestage. As our item-to-semantic-category mapping function(�) can either map items directly to the categories they areassigned to (�

p

) or to the grandparent categories (�g

) wecan form taste profiles of users using two di↵erent categor-ical levels. Our intuition here was that the former profiletype, formed from directly mapped categories, would leadto sparse profiles due to the greater specificity that the cat-egories denote, while the latter profile type, formed fromtransitively mapped grandparent categories would lead todenser taste profiles. This theory was influenced by the priorwork of Ostuni et al. [6], in which the authors consider onlygrandparent categories aligned to semantic URIs.

5.4 Taste Evolution: Local vs Global Dynam-ics

We now turn to looking at the evolution of users’ tastesover time in order to understand how their preferences change.We are interested in examining for two e↵ects: (i) local dy-namics, the propensity for users to develop in their owninimitable manner; and (ii) global dynamics, where usersexhibit consistent development properties. Given our useof probability distributions to model the lifecycle stage spe-cific taste profile of each user, we apply information theo-retic measures based on entropy judgements capturing: (i)consecutive lifecycle stage development, and (ii) informationtransfer between global taste profiles and the local taste pro-files at one lifecycle stage and the taste profiles of the userat the next stage.

5.4.1 Conditional Category Entropy

By using conditional entropy we can assess the informa-tion needed to describe the taste profile of a user at one timestep (Q) using his taste profile from the previous stage (P ).A reduction in conditional entropy indicates that the user’staste profile is similar to that of his previous stage’s pro-file, while an increase indicates the converse. We define theconditional entropy of two discrete probability distributions,representing taste profiles, as:

H(Q|P ) =X

x2P,

y2Q

p(x, y) logp(x)p(x, y)

(5)

We derived the conditional entropy over the 5 lifecycleperiods in a pairwise fashion, i.e. H(P

2

|P1

), . . . , H(P5

|P4

),and plotted the curve of the mean conditional entropy inFigure 5 over each dataset’s users in the training split, alsoincluding the 95% confidence intervals to show the varia-tion in the conditional entropies. Figure 5 indicates thatMovie Lens users tend to diverge in their ratings and cat-egories over time, given the increase in the mean curve to-wards later portions of the users’ lifecycles, the same is alsoevident for Movie Tweetings, however the increase is moregradual there. Amazon users, however, di↵er by showing areduction in conditional entropy towards later lifecycle peri-ods. Relating this back to our above definition of conditionalentropy, the global e↵ect that we see on Amazon indicates

that users tend to converge in their reviewing behaviour andthat previous profiles allow one to gauge how the user willrate items in the future given their category information.Conversely, for MovieLens and Movie Tweetings we see anopposite e↵ect: users’ taste profiles become less predictableas they develop; users rate items in a way that renders un-certainty in profiling from previous information.

0.22

50.

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●

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(c) Amazon

Figure 5: Parent category conditional entropy be-tween consecutive lifecycle stages (e.g. H(P

2

|P3

))across the datasets, together with the bounds of the95% confidence interval for the derived means.

5.4.2 Transfer Category Entropy

Earlier we postulated that the local development of a userand the global development of all users will have di↵erentinfluential e↵ects on certain users, i.e. influencing how theymay review things. We can examine for such e↵ects underthe premise that local development and global developmentare two di↵erent systems, although the former contributesto the latter we would expect a given user who is influencedby what other users rate to be more influenced by globaldevelopment, while users who follow their own path andrate things in their own bespoke manner would eschew suchglobal information. In prior work of Ver Steeg & Aram theauthors adopted transfer entropy to measure informationtransfer in social media [9]. In doing so the authors wereable to assess for influence in retweeting URLs on Twitterbetween users. Transfer entropy is closely related to Grangercausality, and given two time-series signals, allows one tocompare the e↵ect of one on the other.We adopt transfer entropy to assess how the taste profile

(Ps

) of a user at one time step (s) has been influence bylocal (P

s�1

) and global taste (Qs�1

) profiles at the previouslifecycle stage (s�1). For the latter taste profile (Q

s�1

), weform a global probability distribution as above for a singleuser but instead using all users who posted reviews withinthe time interval of s. From these definitions we can thenexamine the information transfer from a prior lifecycle stage(s� 1) to the current lifecycle stage (s) of the user. Now, as-sume that we have a random variable that describe the localcategories that have been reviewed at the current stage (Y

s

),a random variable of local categories at the previous stage(Y

s�1

). and a third random variable of global categories atthe previous stage (X

s�1

), we then define the transfer en-tropy of one lifecycle stage to another as follows, based onthe work of Schreiber [8]:

TX!Y

= H(Ys

|Ys�1

)�H(Ys

|Ys�1

, Xs�1

) (6)

Using the above probability distributions we can calculatethe transfer entropy based on the joint and conditional prob-ability distributions given the values of the random variables

Probability of user rating category c high in lifecycle period s:

From Mining to Understanding: The Evolution of Social Web Users 27

Pr(c|Du,s

train

) =ave rating(Du,s,c

train

)X

c

02C

u,strain

ave rating(Du,s,c

0

train

)(4)

Based on this formalisation we can assess the relativemean rating score per category for a given user and lifecyclestage. As our item-to-semantic-category mapping function(�) can either map items directly to the categories they areassigned to (�

p

) or to the grandparent categories (�g

) wecan form taste profiles of users using two di↵erent categor-ical levels. Our intuition here was that the former profiletype, formed from directly mapped categories, would leadto sparse profiles due to the greater specificity that the cat-egories denote, while the latter profile type, formed fromtransitively mapped grandparent categories would lead todenser taste profiles. This theory was influenced by the priorwork of Ostuni et al. [6], in which the authors consider onlygrandparent categories aligned to semantic URIs.

5.4 Taste Evolution: Local vs Global Dynam-ics

We now turn to looking at the evolution of users’ tastesover time in order to understand how their preferences change.We are interested in examining for two e↵ects: (i) local dy-namics, the propensity for users to develop in their owninimitable manner; and (ii) global dynamics, where usersexhibit consistent development properties. Given our useof probability distributions to model the lifecycle stage spe-cific taste profile of each user, we apply information theo-retic measures based on entropy judgements capturing: (i)consecutive lifecycle stage development, and (ii) informationtransfer between global taste profiles and the local taste pro-files at one lifecycle stage and the taste profiles of the userat the next stage.

5.4.1 Conditional Category Entropy

By using conditional entropy we can assess the informa-tion needed to describe the taste profile of a user at one timestep (Q) using his taste profile from the previous stage (P ).A reduction in conditional entropy indicates that the user’staste profile is similar to that of his previous stage’s pro-file, while an increase indicates the converse. We define theconditional entropy of two discrete probability distributions,representing taste profiles, as:

H(Q|P ) =X

x2P,

y2Q

p(x, y) logp(x)p(x, y)

(5)

We derived the conditional entropy over the 5 lifecycleperiods in a pairwise fashion, i.e. H(P

2

|P1

), . . . , H(P5

|P4

),and plotted the curve of the mean conditional entropy inFigure 5 over each dataset’s users in the training split, alsoincluding the 95% confidence intervals to show the varia-tion in the conditional entropies. Figure 5 indicates thatMovie Lens users tend to diverge in their ratings and cat-egories over time, given the increase in the mean curve to-wards later portions of the users’ lifecycles, the same is alsoevident for Movie Tweetings, however the increase is moregradual there. Amazon users, however, di↵er by showing areduction in conditional entropy towards later lifecycle peri-ods. Relating this back to our above definition of conditionalentropy, the global e↵ect that we see on Amazon indicates

that users tend to converge in their reviewing behaviour andthat previous profiles allow one to gauge how the user willrate items in the future given their category information.Conversely, for MovieLens and Movie Tweetings we see anopposite e↵ect: users’ taste profiles become less predictableas they develop; users rate items in a way that renders un-certainty in profiling from previous information.

0.22

50.

235

0.24

5

Lifecycle Stages

Con

ditio

nal E

ntro

py

●

●

●

●

1 2 3 4 5

(a) Lens

0.27

50.

280

0.28

50.

290

Lifecycle Stages

Con

ditio

nal E

ntro

py

●●

●

●

1 2 3 4 5

(b) Tweetings

0.20

50.

210

0.21

50.

220

Lifecycle Stages

Con

ditio

nal E

ntro

py

●

● ●

●

1 2 3 4 5

(c) Amazon

Figure 5: Parent category conditional entropy be-tween consecutive lifecycle stages (e.g. H(P

2

|P3

))across the datasets, together with the bounds of the95% confidence interval for the derived means.

5.4.2 Transfer Category Entropy

Earlier we postulated that the local development of a userand the global development of all users will have di↵erentinfluential e↵ects on certain users, i.e. influencing how theymay review things. We can examine for such e↵ects underthe premise that local development and global developmentare two di↵erent systems, although the former contributesto the latter we would expect a given user who is influencedby what other users rate to be more influenced by globaldevelopment, while users who follow their own path andrate things in their own bespoke manner would eschew suchglobal information. In prior work of Ver Steeg & Aram theauthors adopted transfer entropy to measure informationtransfer in social media [9]. In doing so the authors wereable to assess for influence in retweeting URLs on Twitterbetween users. Transfer entropy is closely related to Grangercausality, and given two time-series signals, allows one tocompare the e↵ect of one on the other.We adopt transfer entropy to assess how the taste profile

(Ps

) of a user at one time step (s) has been influence bylocal (P

s�1

) and global taste (Qs�1

) profiles at the previouslifecycle stage (s�1). For the latter taste profile (Q

s�1

), weform a global probability distribution as above for a singleuser but instead using all users who posted reviews withinthe time interval of s. From these definitions we can thenexamine the information transfer from a prior lifecycle stage(s� 1) to the current lifecycle stage (s) of the user. Now, as-sume that we have a random variable that describe the localcategories that have been reviewed at the current stage (Y

s

),a random variable of local categories at the previous stage(Y

s�1

). and a third random variable of global categories atthe previous stage (X

s�1

), we then define the transfer en-tropy of one lifecycle stage to another as follows, based onthe work of Schreiber [8]:

TX!Y

= H(Ys

|Ys�1

)�H(Ys

|Ys�1

, Xs�1

) (6)

Using the above probability distributions we can calculatethe transfer entropy based on the joint and conditional prob-ability distributions given the values of the random variables

Conditional-Entropy: relative information difference I.e. how dissimilar is the user’s ratings in period s from period s-1?

From Mining to Understanding: The Evolution of Social Web Users 28

Transfer-Entropy: influence of global behaviour on the user I.e. how does collective user behaviour influence the user’s tastes?

from Ys

, Ys�1

and Xs�1

:

TX!Y

=X

y2Ys,

y

02Ys�1,

x2Xs�1

p(y, y0, x) logp(y|y0, x)p(y|y0)

(7)

We derived the transfer entropy between consecutive life-cycle periods, as with the conditional entropy above, to ex-amine how the influence of global and local dynamics onusers’ taste profiles developed over time. Figure 6 plots themeans of these values across the lifecycle periods togetherwith the 95% confidence intervals. We find that users ofMovieLens transfer entropy decrease over time, indicatingthat global dynamics have a stronger influence on users’taste profiles towards later lifecycle stages. Such an e↵ect ischaracteristic of users becoming more involved and familiarwith the review system, and as a consequence paying atten-tion to more information from the users. With Movie Tweet-ings and Amazon we find a di↵erent e↵ect: users’ transferentropy actually increases over time, indicating that usersare less influenced by global taste preferences, and thereforethe ratings of other users, and instead concentrate on theirown tastes.

0.12

00.

122

0.12

4

Lifecycle Stages

Tran

sfer

Ent

ropy ●

●

●

●

1 2 3 4 5

(a) Lens

0.11

20.

114

0.11

6

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(b) Tweetings

0.13

00.

132

0.13

40.

136

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(c) Amazon

Figure 6: Parent category transfer entropy betweenconsecutive lifecycle stages (e.g. H(P

2

|P3

)) across thedatasets, together with the bounds of the 95% con-fidence interval for the derived means.

6. RECOMMENDATIONSFindings from the previous section indicate a link be-

tween lifecycle duration and taste evolution across the plat-form: -Entropy: users’ tastes profile reduce in variation onMovieLens, reduce then go up on Tweetings, and increasethen decrease on Amazon -Conditional Entropy: Lens andTweetings show that users diverge in their tastes consecu-tively, while Amazon users converge -Transfer Entropy: Lensusers are more strongly influenced by global tastes over time,while Tweetings users are less influenced by global tastesover time, while Amazon...

Hence time has a strong e↵ect on the taste profile of theuser and the likelihood of him rating an item from a givencategory positively

6.1 Recommendation Model FormulationWe use the following model for our recommender system

based upon matrix factorisation:

rui

= bui

+ p|u

qi

(8)

6.2 BiasesThe biases in our model are defined as follows:

bui

=

Staticz }| {µ+ b

i

+ bu

+

Evolvingz }| {bi,cats(i)

+ bu,cats(i)

(9)

6.2.1 Static Biases

The bias component of our model contains static biases in-duced from the training segment. There include the generalbias of the given dataset (µ), which is shown in Figure 7 asthe mean rating score across all ratings within the trainingsegment. The use of the mean on its own is insu�cient - i.e.note the variance in ratings scores for the Amazon Moviesdataset - therefore we also include the item bias (b

i

) andthe user bias (b

u

). The former bias is the average deviationfrom the mean bias for the item i within the training seg-ment, while the latter bias is the average deviation from themean bias from the training segment’s ratings by user u.

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p(x)

1 2 3 4 5

10−4

10−3

10−2 µ=3.7

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p(x)

1 2 3 4 5 6 7 8 9

10−5

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100

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●

Lifetime (in days) per user

p(x)

1 2 3 4 5

10−8

10−6

10−4

100

µ=4.1

(c) Amazon

Figure 7: Distribution of users’ ratings across thethree datasets

6.2.2 Category Biases

Item Biases Towards Categories.

Item bias given the categories-Evolution of the category biases in the training segment,

anticipated evolution into the test segment -Using globaltaste profiles to work this outWant to capture the proportional change in category rat-

ings across the entire platform, to do this we derive thedevelopment of all users’ preference for a given category cthroughout the training segment, where Q

s

is the globaltaste profile (discrete probability distribution of all cate-gories):

�c

=1

4� k

4X

s=k

Qs+1

(c)�Qs

(c)Q

s

(c)(10)

From this we can then calculate the conditional probabil-ity of a given category being rated highly within the testsegment by accounting for the change rate of rating prefer-ence for the category as follows:

Pr(+|c) =Prior Ratingz }| {Q

5

(c) +

Change Ratez }| {�

c

Q5

(c) (11)

Thereby, by averaging this over all categories for the itemi can can calculate the evolving item bias from the trainingsegment:

bi,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c) (12)

Current Work!

From Mining to Understanding: The Evolution of Social Web Users 29

from Ys

, Ys�1

and Xs�1

:

TX!Y

=X

y2Ys,

y

02Ys�1,

x2Xs�1

p(y, y0, x) logp(y|y0, x)p(y|y0)

(7)

We derived the transfer entropy between consecutive life-cycle periods, as with the conditional entropy above, to ex-amine how the influence of global and local dynamics onusers’ taste profiles developed over time. Figure 6 plots themeans of these values across the lifecycle periods togetherwith the 95% confidence intervals. We find that users ofMovieLens transfer entropy decrease over time, indicatingthat global dynamics have a stronger influence on users’taste profiles towards later lifecycle stages. Such an e↵ect ischaracteristic of users becoming more involved and familiarwith the review system, and as a consequence paying atten-tion to more information from the users. With Movie Tweet-ings and Amazon we find a di↵erent e↵ect: users’ transferentropy actually increases over time, indicating that usersare less influenced by global taste preferences, and thereforethe ratings of other users, and instead concentrate on theirown tastes.

0.12

00.

122

0.12

4

Lifecycle Stages

Tran

sfer

Ent

ropy ●

●

●

●

1 2 3 4 5

(a) Lens

0.11

20.

114

0.11

6

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(b) Tweetings

0.13

00.

132

0.13

40.

136

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(c) Amazon

Figure 6: Parent category transfer entropy betweenconsecutive lifecycle stages (e.g. H(P

2

|P3

)) across thedatasets, together with the bounds of the 95% con-fidence interval for the derived means.

6. RECOMMENDATIONSFindings from the previous section indicate a link be-

tween lifecycle duration and taste evolution across the plat-form: -Entropy: users’ tastes profile reduce in variation onMovieLens, reduce then go up on Tweetings, and increasethen decrease on Amazon -Conditional Entropy: Lens andTweetings show that users diverge in their tastes consecu-tively, while Amazon users converge -Transfer Entropy: Lensusers are more strongly influenced by global tastes over time,while Tweetings users are less influenced by global tastesover time, while Amazon...

Hence time has a strong e↵ect on the taste profile of theuser and the likelihood of him rating an item from a givencategory positively

6.1 Recommendation Model FormulationWe use the following model for our recommender system

based upon matrix factorisation:

rui

= bui

+ p|u

qi

(8)

6.2 BiasesThe biases in our model are defined as follows:

bui

=

Staticz }| {µ+ b

i

+ bu

+

Evolvingz }| {bi,cats(i)

+ bu,cats(i)

(9)

6.2.1 Static Biases

The bias component of our model contains static biases in-duced from the training segment. There include the generalbias of the given dataset (µ), which is shown in Figure 7 asthe mean rating score across all ratings within the trainingsegment. The use of the mean on its own is insu�cient - i.e.note the variance in ratings scores for the Amazon Moviesdataset - therefore we also include the item bias (b

i

) andthe user bias (b

u

). The former bias is the average deviationfrom the mean bias for the item i within the training seg-ment, while the latter bias is the average deviation from themean bias from the training segment’s ratings by user u.

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p(x)

1 2 3 4 5

10−4

10−3

10−2 µ=3.7

(a) Lens

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p(x)

1 2 3 4 5 6 7 8 9

10−5

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100

µ=7.7

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●

Lifetime (in days) per user

p(x)

1 2 3 4 5

10−8

10−6

10−4

100

µ=4.1

(c) Amazon

Figure 7: Distribution of users’ ratings across thethree datasets

6.2.2 Category Biases

Item Biases Towards Categories.

Item bias given the categories-Evolution of the category biases in the training segment,

anticipated evolution into the test segment -Using globaltaste profiles to work this outWant to capture the proportional change in category rat-

ings across the entire platform, to do this we derive thedevelopment of all users’ preference for a given category cthroughout the training segment, where Q

s

is the globaltaste profile (discrete probability distribution of all cate-gories):

�c

=1

4� k

4X

s=k

Qs+1

(c)�Qs

(c)Q

s

(c)(10)

From this we can then calculate the conditional probabil-ity of a given category being rated highly within the testsegment by accounting for the change rate of rating prefer-ence for the category as follows:

Pr(+|c) =Prior Ratingz }| {Q

5

(c) +

Change Ratez }| {�

c

Q5

(c) (11)

Thereby, by averaging this over all categories for the itemi can can calculate the evolving item bias from the trainingsegment:

bi,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c) (12)

from Ys

, Ys�1

and Xs�1

:

TX!Y

=X

y2Ys,

y

02Ys�1,

x2Xs�1

p(y, y0, x) logp(y|y0, x)p(y|y0)

(7)

We derived the transfer entropy between consecutive life-cycle periods, as with the conditional entropy above, to ex-amine how the influence of global and local dynamics onusers’ taste profiles developed over time. Figure 6 plots themeans of these values across the lifecycle periods togetherwith the 95% confidence intervals. We find that users ofMovieLens transfer entropy decrease over time, indicatingthat global dynamics have a stronger influence on users’taste profiles towards later lifecycle stages. Such an e↵ect ischaracteristic of users becoming more involved and familiarwith the review system, and as a consequence paying atten-tion to more information from the users. With Movie Tweet-ings and Amazon we find a di↵erent e↵ect: users’ transferentropy actually increases over time, indicating that usersare less influenced by global taste preferences, and thereforethe ratings of other users, and instead concentrate on theirown tastes.

0.12

00.

122

0.12

4

Lifecycle Stages

Tran

sfer

Ent

ropy ●

●

●

●

1 2 3 4 5

(a) Lens

0.11

20.

114

0.11

6

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(b) Tweetings

0.13

00.

132

0.13

40.

136

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(c) Amazon

Figure 6: Parent category transfer entropy betweenconsecutive lifecycle stages (e.g. H(P

2

|P3

)) across thedatasets, together with the bounds of the 95% con-fidence interval for the derived means.

6. RECOMMENDATIONSFindings from the previous section indicate a link be-

tween lifecycle duration and taste evolution across the plat-form: -Entropy: users’ tastes profile reduce in variation onMovieLens, reduce then go up on Tweetings, and increasethen decrease on Amazon -Conditional Entropy: Lens andTweetings show that users diverge in their tastes consecu-tively, while Amazon users converge -Transfer Entropy: Lensusers are more strongly influenced by global tastes over time,while Tweetings users are less influenced by global tastesover time, while Amazon...

Hence time has a strong e↵ect on the taste profile of theuser and the likelihood of him rating an item from a givencategory positively

6.1 Recommendation Model FormulationWe use the following model for our recommender system

based upon matrix factorisation:

rui

= bui

+ p|u

qi

(8)

6.2 BiasesThe biases in our model are defined as follows:

bui

=

Staticz }| {µ+ b

i

+ bu

+

Evolvingz }| {bi,cats(i)

+ bu,cats(i)

(9)

6.2.1 Static Biases

The bias component of our model contains static biases in-duced from the training segment. There include the generalbias of the given dataset (µ), which is shown in Figure 7 asthe mean rating score across all ratings within the trainingsegment. The use of the mean on its own is insu�cient - i.e.note the variance in ratings scores for the Amazon Moviesdataset - therefore we also include the item bias (b

i

) andthe user bias (b

u

). The former bias is the average deviationfrom the mean bias for the item i within the training seg-ment, while the latter bias is the average deviation from themean bias from the training segment’s ratings by user u.

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p(x)

1 2 3 4 5

10−4

10−3

10−2 µ=3.7

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Average Rating

p(x)

1 2 3 4 5 6 7 8 9

10−5

10−4

10−3

10−2

10−1

100

µ=7.7

(b) Tweetings

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●

Lifetime (in days) per user

p(x)

1 2 3 4 5

10−8

10−6

10−4

100

µ=4.1

(c) Amazon

Figure 7: Distribution of users’ ratings across thethree datasets

6.2.2 Category Biases

Item Biases Towards Categories.

Item bias given the categories-Evolution of the category biases in the training segment,

anticipated evolution into the test segment -Using globaltaste profiles to work this outWant to capture the proportional change in category rat-

ings across the entire platform, to do this we derive thedevelopment of all users’ preference for a given category cthroughout the training segment, where Q

s

is the globaltaste profile (discrete probability distribution of all cate-gories):

�c

=1

4� k

4X

s=k

Qs+1

(c)�Qs

(c)Q

s

(c)(10)

From this we can then calculate the conditional probabil-ity of a given category being rated highly within the testsegment by accounting for the change rate of rating prefer-ence for the category as follows:

Pr(+|c) =Prior Ratingz }| {Q

5

(c) +

Change Ratez }| {�

c

Q5

(c) (11)

Thereby, by averaging this over all categories for the itemi can can calculate the evolving item bias from the trainingsegment:

bi,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c) (12)

Including Taste Evolution in a Recommender System

User Biases Towards Categories.

Recap that in the previous section when analysing thechanges in taste profiles over the lifecycle stages, we inducedper-user discrete probability distributions that captured theprobability of the u rating a given category c highly duringlifecycle stage s: Pu

s

(c). Given that users’ taste evolve, ourgoal is to estimate the probability of the user rating an itemhighly given its categories by capturing three things: (i) howuser rated categories during the last observed lifecycle stagein the training segment (Pu

5

); (ii) how the user’s preferencesfor each category has changed in past, either decaying orgrowing, informed from the category entropy; and (iii) thesusceptibility of the user to global taste changes, and thushow other users have rated the categories.

To capture the development of a user’s preference for acategory we derive the average change rate (�u

c

) over thek lifecycle periods coming before the final lifecycle stage inthe training set. The parameter k is the number of stagesback in the training segment from which either a monotonicincrease or decrease in the probability of rating category cbegan from. We define the change rate (�u

c

) as follows:

�u

c

=1

4� k

4X

s=k

Pu

s+1

(c)� Pu

s

(c)

Pu

s

(c)(13)

In a similar vein, we also capture the influence of globaldynamics of the user’s taste profile. We found in the previ-ous section that the transfer entropy of the users across allthree platforms either reduced or increased as users’ lifecy-cles increased, indicating an increase and decrease of influ-ence by global taste dynamics respectively. We can capturesuch signals on a per-user basis by assessing the change intransfer entropy for each user over time and modelling thisas a global influence factor �u. We derive this as follows,based on measuring the proportional change in transfer en-tropy starting from lifecycle period k that produced a mono-tonic increase or decrease in transfer entropy:

�u =1

4� k

4X

s=k

Ts+1|sQ!P

� Ts|s�1

Q!P

Ts|s�1

Q!P

(14)

By combining the average change rate of the user highlyrating the category (�u

c

) with the global influence factor �u,we can derive the anticipated per-category bias for the useras follows, where Pu

5

denotes the taste profile of the userobserved for the final lifecycle stage (5):

Pr(+|c, u) =Prior Ratingz }| {Pu

5

(c) +

Change Ratez }| {�u

c

Pu

5

(c) +

Global Influencez }| {�uQ

5

(c) (15)

Given that a single item can be linked to many categorieson the the web of linked data, we take the average across allcategories as the bias of the user given the categories of theitem:

bu,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c, u) (16)

Although the above summation will quantify the bias forcategories linked to item i for which the user has provideda rating beforehand, the bias will ignore any categories forwhich the user has yet to provide ratings. To counteractthis we use a lateral transfer function (g) that incorporatesthe most similar category that the user u has rated an itemfrom. This is one of the advantages of using linked data: as

the categories form a taxonomic hierarchy built up from spe-cialisation relations, we can measure the distance betweeneach category linked to the item c 2 cats(i) to each cate-gory that the user has rated beforehand (c0 2 cats(Du,5

train

)),and choose the category with the minimum distance as therepresentative category to use instead:

g(c) = argminc

02cats(D

u,5train)

d(c, c0) (17)

For the distance function we used the Bellman-Ford al-gorithm to calculate shortest paths through the categorygraph. We derived the relative complement of the set ofcategories for which u has rated an item with the set of cate-gories which item i is placed in as C0 = cats(Du,5

train

)/cats(i),and the intersection of the set categories from the user’srated items and the set of categories for item i as C00 =cats(Du,5

train

) \ cats(i). This now allows for our earlier def-inition of the bias of the user u towards the categories ofitem i to be modified to account for unrated categories asfollows:

bu,cats(i)

=

Lateral Categoriesz }| {1

|C0|X

c2C

0

Pr(+|g(c), u) +

Prior Rated Categoriesz }| {1

|C00|X

c2C

00

Pr(+|c, u)

(18)

6.3 Combining Latent Factors and SemanticCategories

Our recommendation model combines biases, both staticand evolutionary, together with the personalisation prefer-ences of the user mined from their past ratings. We buildon existing work from recommender systems domain and inparticular the work of Yehuda Koren on SVD++ [4]. In Ko-ren’s prior work, which is now one of the most widely usedmethods of applying Matrix Factorisation to collaborativefiltering, the past ratings of the user are included within thepersonalisation component of the recommendation model asfollows:

rui

= bui

+ q|i

�pu

+ |R(u)|�12

X

j2R(u)

yj

�(19)

Above, we have three latent factor vectors: qi

2 Rf de-notes the f latent factors associated with the item i; p

u

2 Rf

denotes the f latent factors associated with the user u; andyj

2 Rf denotes the f dimension latent factor vector foritem j from the set of rated items by user u: R(u). The la-tent factors are derived during learning, as we shall explainbelow, while the number of factors to capture (f) is set a pri-ori - this is often set to 50 across the literature. The factorscapture unifying attributes across the items, for instance Ro-mantic Comedies or Action Films in the movies domain. Weextend Equation 19 to incorporate latent factors for each se-mantic category that a user has rated an item from. Our in-tuition behind this inclusion is that certain categories have astronger a�nity with certain factors, for instance the DBPe-dia category category:1970s_science_fiction_films willhave a strong a�nity with the latent factor corresponding toScience Fiction films. By including this information we an-ticipated that additional cues for user preferences, function-ing at between the semantic categories and latent factors,would be captured.We adapted the above model to derive Equation 20. Here

we have defined a new vector zc

2 Rf which captures the

User Biases Towards Categories.

Recap that in the previous section when analysing thechanges in taste profiles over the lifecycle stages, we inducedper-user discrete probability distributions that captured theprobability of the u rating a given category c highly duringlifecycle stage s: Pu

s

(c). Given that users’ taste evolve, ourgoal is to estimate the probability of the user rating an itemhighly given its categories by capturing three things: (i) howuser rated categories during the last observed lifecycle stagein the training segment (Pu

5

); (ii) how the user’s preferencesfor each category has changed in past, either decaying orgrowing, informed from the category entropy; and (iii) thesusceptibility of the user to global taste changes, and thushow other users have rated the categories.

To capture the development of a user’s preference for acategory we derive the average change rate (�u

c

) over thek lifecycle periods coming before the final lifecycle stage inthe training set. The parameter k is the number of stagesback in the training segment from which either a monotonicincrease or decrease in the probability of rating category cbegan from. We define the change rate (�u

c

) as follows:

�u

c

=1

4� k

4X

s=k

Pu

s+1

(c)� Pu

s

(c)

Pu

s

(c)(13)

In a similar vein, we also capture the influence of globaldynamics of the user’s taste profile. We found in the previ-ous section that the transfer entropy of the users across allthree platforms either reduced or increased as users’ lifecy-cles increased, indicating an increase and decrease of influ-ence by global taste dynamics respectively. We can capturesuch signals on a per-user basis by assessing the change intransfer entropy for each user over time and modelling thisas a global influence factor �u. We derive this as follows,based on measuring the proportional change in transfer en-tropy starting from lifecycle period k that produced a mono-tonic increase or decrease in transfer entropy:

�u =1

4� k

4X

s=k

Ts+1|sQ!P

� Ts|s�1

Q!P

Ts|s�1

Q!P

(14)

By combining the average change rate of the user highlyrating the category (�u

c

) with the global influence factor �u,we can derive the anticipated per-category bias for the useras follows, where Pu

5

denotes the taste profile of the userobserved for the final lifecycle stage (5):

Pr(+|c, u) =Prior Ratingz }| {Pu

5

(c) +

Change Ratez }| {�u

c

Pu

5

(c) +

Global Influencez }| {�uQ

5

(c) (15)

Given that a single item can be linked to many categorieson the the web of linked data, we take the average across allcategories as the bias of the user given the categories of theitem:

bu,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c, u) (16)

Although the above summation will quantify the bias forcategories linked to item i for which the user has provideda rating beforehand, the bias will ignore any categories forwhich the user has yet to provide ratings. To counteractthis we use a lateral transfer function (g) that incorporatesthe most similar category that the user u has rated an itemfrom. This is one of the advantages of using linked data: as

the categories form a taxonomic hierarchy built up from spe-cialisation relations, we can measure the distance betweeneach category linked to the item c 2 cats(i) to each cate-gory that the user has rated beforehand (c0 2 cats(Du,5

train

)),and choose the category with the minimum distance as therepresentative category to use instead:

g(c) = argminc

02cats(D

u,5train)

d(c, c0) (17)

For the distance function we used the Bellman-Ford al-gorithm to calculate shortest paths through the categorygraph. We derived the relative complement of the set ofcategories for which u has rated an item with the set of cate-gories which item i is placed in as C0 = cats(Du,5

train

)/cats(i),and the intersection of the set categories from the user’srated items and the set of categories for item i as C00 =cats(Du,5

train

) \ cats(i). This now allows for our earlier def-inition of the bias of the user u towards the categories ofitem i to be modified to account for unrated categories asfollows:

bu,cats(i)

=

Lateral Categoriesz }| {1

|C0|X

c2C

0

Pr(+|g(c), u) +

Prior Rated Categoriesz }| {1

|C00|X

c2C

00

Pr(+|c, u)

(18)

6.3 Combining Latent Factors and SemanticCategories

Our recommendation model combines biases, both staticand evolutionary, together with the personalisation prefer-ences of the user mined from their past ratings. We buildon existing work from recommender systems domain and inparticular the work of Yehuda Koren on SVD++ [4]. In Ko-ren’s prior work, which is now one of the most widely usedmethods of applying Matrix Factorisation to collaborativefiltering, the past ratings of the user are included within thepersonalisation component of the recommendation model asfollows:

rui

= bui

+ q|i

�pu

+ |R(u)|�12

X

j2R(u)

yj

�(19)

Above, we have three latent factor vectors: qi

2 Rf de-notes the f latent factors associated with the item i; p

u

2 Rf

denotes the f latent factors associated with the user u; andyj

2 Rf denotes the f dimension latent factor vector foritem j from the set of rated items by user u: R(u). The la-tent factors are derived during learning, as we shall explainbelow, while the number of factors to capture (f) is set a pri-ori - this is often set to 50 across the literature. The factorscapture unifying attributes across the items, for instance Ro-mantic Comedies or Action Films in the movies domain. Weextend Equation 19 to incorporate latent factors for each se-mantic category that a user has rated an item from. Our in-tuition behind this inclusion is that certain categories have astronger a�nity with certain factors, for instance the DBPe-dia category category:1970s_science_fiction_films willhave a strong a�nity with the latent factor corresponding toScience Fiction films. By including this information we an-ticipated that additional cues for user preferences, function-ing at between the semantic categories and latent factors,would be captured.We adapted the above model to derive Equation 20. Here

we have defined a new vector zc

2 Rf which captures the

•  Predict rating for user u for item i:

Bias component of user u and item i

Personalisation component: f latent factors

•  Modify bias component to include taste evolution signal:

•  Interpolate categories within the personalisation component:

Too much maths to be shown here!

How global tastes for the categories of item i have evolved

How the tastes of user u have evolved for categories of item i

From Mining to Understanding: The Evolution of Social Web Users 30

By modelling taste evolution we can capture…

(i)  the influence of global dynamics on the user (ii)  how the user’s preferences for categories change

(iii)  how global tastes are evolving

Table 2: Statistics of the revised review datasets used for our analysis and experiments. Reduction over theoriginal datasets are shown in parentheses.

Dataset #Users #Items #RatingsMovieLens 6,024 (-0%) 3,231 (-12.1%) 841,602 (-6.7%)Movie Tweetings 17,827 (-6.3%) 7,913 (-30.8%) 104,055 (-11.2%)Amazon 444,861 (-49.9%) 27,066 (-89.4%) 5,564,199 (-29.3%)Total 468,712 (-48.7%) 38,210 (-85.7%) 6,509,856 (-26.9%)

sion programmes. Again, we find that obscure films such as‘Cry of the Black Wolves’ was not aligned to a semantic URIdespite it having a IMDB page. We define the challenge ofaddressing the obscurity of movies, and thus their lack of aDBPedia entry, as the hipster dilemma. In the discussionssection of the paper we outline several strategies for deal-ing with this in the future given its presence not only inthis work but in the prior work of Ostuni et al. [6], and itpotential e↵ect on future work within this domain.

4.3.1 Category Ratings

To provide a first look into to the link between seman-tic categories and ratings, we examined the average ratingsof the top-2 most frequently reviewed categories across thedatasets. This was derived by recording the frequency ofcategories linked to by rated items within the training split,and then selecting the top-2 most frequent. In Figure 3 weplotted the development of the average rating score acrossthese two categories, derived using a 7-day moving averageto smooth the variance in rating fluctuations. We find thatthere are peaks and troughs in the reviewing of the itemsthat belong to the categories, in particular one can note thatfor MovieLens the scores remain relatively stable, while forMovie Tweetings ‘Independent Films’ reduce in their averagerating and ‘Directorial Debut films’ increase in their averagerating over time. Such information can be encoded withinthe biases of the recommendation models and consider thestability of a given bias in light of when the rating is beingmade: i.e. considering the fluctuation of the rating signaland how this relates to previous fluctuations.

May Jul Sep Nov

3.0

3.2

3.4

3.6

3.8

4.0

Time

Aver

age

Rat

ing

Directorial Debut Films1990s Comedy Films

(a) Lens

Mar Apr May Jun Jul Aug

5.0

6.0

7.0

8.0

Time

Aver

age

Rat

ing

Independent FilmsDirectorial Debut Films

(b) Tweetings

1998 2002 2006 2010

01

23

45

Time

Aver

age

Rat

ing

American FilmsBlack and White Films

(c) Amazon

Figure 3: Average ratings derived using a 7-daymoving average of the top-2 most frequently ratedcategories.

5. ANALYSING TASTE EVOLUTIONAnalysing the evolution and development of users’ tastes

allows one to understand how a given user is likely to ratea given item in the future. In the context of this paper we

concentrate on movie items; this domain is unique for en-compassing a variety of genres, where movies can be placedin categories (as described above). We are interested in try-ing to understand three things: (i) global evolution dynam-ics, describing how users in general transition and developin their preferences over time; (ii) local evolution dynamics,in terms of how a specific user is evolving his tastes; andfinally (iii) the association between global and local dynam-ics. This latter aspect concerns the influence that generaltrends of taste evolution have on a given user: we postulatethat certain users will be more greatly influenced by suchdynamics than others, and this is something that we controlfor in our recommendation model which follows this section.In this section we analyse for global and local dynamics, andmine the relation between local and global dynamics in in-fluencing users’ tastes. In particular, given our use of threedi↵erent datasets derived from three distinct sources, we areinterested in understanding how local and global taste evo-lution di↵ers, and the influence that one has on the otherfor the platforms’ users.

5.1 Preamble: NotationFrom this point onwards we are entering the realm of rec-

ommender systems, and therefore to aid comprehension andease of legibility we reserve the following special charactersfor set notations, as follows:

• u, v denote users• i, j denote items• r denotes a known rating value (where r 2 R), and r

denotes a predicted rating value• Datasets are provided as quadruples of the form (u, i, r, t) 2

D and are segmented into training (Dtrain

) and testing(D

test

) datasets by the above mentioned cuto↵ pointssuch that D

train

\Dtest

= ;• c, c0 denote category concepts within the linked data

graph and C denotes the set of categories. The graphitself is denoted by: G = hC,Ei, where e

c,c

0 2 E de-notes the set of edges, or concept relations, that con-nect concepts together within the graph. We use a di-rected graph and only consider hierarchical relations:i.e. e

c,c

0 denotes the edge connecting c and c0 throughthe triple c skos:broader c0 such that c has a broader,and thus more general category, denoted by c0.

• � denotes a mapping function between items and se-mantic categories, realised through the disambigua-tion of semantic URIs for items. The mapping func-tion either maps items to their direct parent cate-gories: �

p

: I⇥C;3 or maps items to their transitively-connected grandparent categories: �

g

: I ⇥ C.4

3I.e. Using the statement: i dcterms:subject c4I.e. Via: i dcterms:subject ?p, ?p skos:broader c

Conclusions 31

From Mining to Understanding: The Evolution of Social Web Users

From Mining to Understanding: The Evolution of Social Web Users 32

1.  User evolution can be captured using lifecycle models

2.  Churners and non-churners exhibit divergent signals

3.  Users’ tastes are susceptible to global taste influence

1 2 3 … n

rive the probability distribution, we instead used all posts.For instance, for the global in-degree distribution we usedthe frequencies of received messages for all users. Given thediscrete probability distribution of a user from a time inter-val (P[t,t0]), and the global probability distribution over thesame time interval (Q[t,t0]), we derived the cross-entropy asabove between the distributions. (H(P[t,t0], Q[t,t0])).

Again, as with period cross-entropies, we find churners’signals to have a lower magnitude than non-churners sug-gesting that non-churners’ properties tend to diverge fromthe community as they progress throughout their lifetimewithin the online community platforms. There are some no-ticeably noisy signals however, in particular for Facebookand the in-degree distribution and lexical term distributionsof non-churners. Generally for each signal we see a growingcurve towards later lifecycle periods for both churners andnon-churners, while the magnitudes of the curves are thesalient di↵erentiating feature.

●

●

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0.2

0.4

0.6

0.8

1.0

1.2

Lifecycle Stages

Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

● ChurnersNon−churners

(a) In-degree -Facebook

● ● ●●

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●

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●

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●

●

3.0

3.5

4.0

4.5

5.0

Lifecycle Stages

Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(b) In-degree -SAP

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0.5

1.0

1.5

2.0

2.5

Lifecycle Stages

Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(c) In-degree -Server Fault

●

●

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●

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●

2.0

2.5

3.0

3.5

4.0

Lifecycle Stages

Com

mun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(d) Out-degree -Facebook

● ● ●●

●●

● ● ●●

● ●●

●

●

● ●●

●

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Lifecycle StagesC

omm

unity

Cro

ss E

ntro

py

0 0.2 0.4 0.6 0.8 1

(e) Out-degree -SAP

●●

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●

● ●●

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●

3.0

3.5

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4.5

5.0

5.5

6.0

Lifecycle Stages

Com

mun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(f) Out-degree -Server Fault

●

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6.0

6.2

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7.0

Lifecycle Stages

Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(g) Lexical - Face-book

● ●●

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6.5

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7.5

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Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(h) Lexical - SAP

●

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7.0

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8.5

Lifecycle Stages

Com

umun

ity C

ross

Ent

ropy

0 0.2 0.4 0.6 0.8 1

(i) Lexical - ServerFault

Figure 4: Community cross-entropy comparingchurners with non-churners along: in-degree (Fig-ure 4(a); 4(b); and 4(c)), out-degree (Figure 4(d);4(e); and 4(f)) and lexical term distributions (Fig-ure 4(g); 3(h); and 4(i)).

5. CHURN PREDICTION MODELOur analysis of the di↵erences between churners and non-

churners exposed latent descriptions and signals of how thesegroups of users develop throughout their lifecycles, findingdi↵erent development signals in terms of each measure’s

magnitude and rate of change. In this section we turn tothe problem of engineering a model to predict churners byusing our prior insights to build features.

5.1 Feature EngineeringOur analysis results indicate that churners and non-churners

di↵ered between one another in terms of: (i) decay ratesfor certain measures, i.e. out-degree period cross-entropy;and (ii) the magnitude of features, i.e. lexical period cross-entropy. Therefore we define two types of features that ourprediction model uses: (i) rates and (ii) magnitudes, whereeach feature is measured for a given lifecycle period. To easefeature definition and model specification, we alter the life-cycle period notation from the existing interval tuple set (i.e.[t, t0] 2 T ) to use a set of discrete single elements: s 2 S,where S = {1, 2, . . . , 20}. Magnitude features are definedas a given user’s measure taken at a given lifecycle period:m(u, s), where the measure for user u is taken at lifecycleperiod s. Rates are defined as changes in measures from onelifecycle period to the next:

�m(u, s) =dm

ds=

m(u, s+ 1)�m(u, s)m(u, s)

(5)

Where �m is indexed by the given measure (i.e. in-degreeperiod cross-entropy), using the above magnitude functionto return the magnitude of a given measure (m) for user uat the allotted lifecycle period. Thus a feature vector (x)is formed for a single user using these rate and magnitudefeatures:

x =[m1(u, 2), . . . ,m1(u, 19),m2(u, 2), . . . ,m2(u, 19), . . .

�m1(u, 2), . . . , �m1(u, 18), �m2(u, 1), . . . , �m2(u, 18)]

As a result of using both rates and magnitudes from eachof the 20 lifecycle periods, aside from the first and last onefor magnitudes and the first and last two for rates, we areprovided with at most 210 features, given the provision of18 magnitude features for each of the 6 measures and 17rate features for each of the 6 measures. As we will de-scribe within the experiments section, we vary the featuresused between di↵erent: (i) feature sets, i.e. in-degree basedfeatures, community cross-entropy based features, etc.; and(ii) lifecycle periods. On this latter aspect we address one ofthe research questions that has driven this work: how earlyinto a user’s lifecycle can we predict them churning? Byconstraining the features to early time periods and thus it-eratively increasing the number of features to use, and hencethe lifecycle periods that the user’s information covers, wedemonstrate the earliest point, for each platform, at whichwe can accurately predict churners.

5.2 Model Definition and LearningWe are provided with, for each of our three online com-

munity platforms, a training dataset and a testing dataseteach taking the following form: {(xi, yi)} 2 D, where xi

defines the feature vector of user ui and yi defines the classlabel of the user, taking a value from the set {0, 1}: 1 ifthe user churned and 0 otherwise. In defining the predic-tion model our goal was to induce a function that predictsthe probability of churning based on a user’s feature vectorf : Rn ! [0, 1]. We define this function as follows for anarbitrary feature vector x and learnt model weights (w) as

from Ys

, Ys�1

and Xs�1

:

TX!Y

=X

y2Ys,

y

02Ys�1,

x2Xs�1

p(y, y0, x) logp(y|y0, x)p(y|y0)

(7)

We derived the transfer entropy between consecutive life-cycle periods, as with the conditional entropy above, to ex-amine how the influence of global and local dynamics onusers’ taste profiles developed over time. Figure 6 plots themeans of these values across the lifecycle periods togetherwith the 95% confidence intervals. We find that users ofMovieLens transfer entropy decrease over time, indicatingthat global dynamics have a stronger influence on users’taste profiles towards later lifecycle stages. Such an e↵ect ischaracteristic of users becoming more involved and familiarwith the review system, and as a consequence paying atten-tion to more information from the users. With Movie Tweet-ings and Amazon we find a di↵erent e↵ect: users’ transferentropy actually increases over time, indicating that usersare less influenced by global taste preferences, and thereforethe ratings of other users, and instead concentrate on theirown tastes.

0.12

00.

122

0.12

4

Lifecycle Stages

Tran

sfer

Ent

ropy ●

●

●

●

1 2 3 4 5

(a) Lens

0.11

20.

114

0.11

6

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(b) Tweetings

0.13

00.

132

0.13

40.

136

Lifecycle Stages

Tran

sfer

Ent

ropy

● ●●

●

1 2 3 4 5

(c) Amazon

Figure 6: Parent category transfer entropy betweenconsecutive lifecycle stages (e.g. H(P

2

|P3

)) across thedatasets, together with the bounds of the 95% con-fidence interval for the derived means.

6. RECOMMENDATIONSFindings from the previous section indicate a link be-

tween lifecycle duration and taste evolution across the plat-form: -Entropy: users’ tastes profile reduce in variation onMovieLens, reduce then go up on Tweetings, and increasethen decrease on Amazon -Conditional Entropy: Lens andTweetings show that users diverge in their tastes consecu-tively, while Amazon users converge -Transfer Entropy: Lensusers are more strongly influenced by global tastes over time,while Tweetings users are less influenced by global tastesover time, while Amazon...

Hence time has a strong e↵ect on the taste profile of theuser and the likelihood of him rating an item from a givencategory positively

6.1 Recommendation Model FormulationWe use the following model for our recommender system

based upon matrix factorisation:

rui

= bui

+ p|u

qi

(8)

6.2 BiasesThe biases in our model are defined as follows:

bui

=

Staticz }| {µ+ b

i

+ bu

+

Evolvingz }| {bi,cats(i)

+ bu,cats(i)

(9)

6.2.1 Static Biases

The bias component of our model contains static biases in-duced from the training segment. There include the generalbias of the given dataset (µ), which is shown in Figure 7 asthe mean rating score across all ratings within the trainingsegment. The use of the mean on its own is insu�cient - i.e.note the variance in ratings scores for the Amazon Moviesdataset - therefore we also include the item bias (b

i

) andthe user bias (b

u

). The former bias is the average deviationfrom the mean bias for the item i within the training seg-ment, while the latter bias is the average deviation from themean bias from the training segment’s ratings by user u.

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Average Rating

p(x)

1 2 3 4 5

10−4

10−3

10−2 µ=3.7

(a) Lens

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Average Rating

p(x)

1 2 3 4 5 6 7 8 9

10−5

10−4

10−3

10−2

10−1

100

µ=7.7

(b) Tweetings

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●

Lifetime (in days) per user

p(x)

1 2 3 4 5

10−8

10−6

10−4

100

µ=4.1

(c) Amazon

Figure 7: Distribution of users’ ratings across thethree datasets

6.2.2 Category Biases

Item Biases Towards Categories.

Item bias given the categories-Evolution of the category biases in the training segment,

anticipated evolution into the test segment -Using globaltaste profiles to work this outWant to capture the proportional change in category rat-

ings across the entire platform, to do this we derive thedevelopment of all users’ preference for a given category cthroughout the training segment, where Q

s

is the globaltaste profile (discrete probability distribution of all cate-gories):

�c

=1

4� k

4X

s=k

Qs+1

(c)�Qs

(c)Q

s

(c)(10)

From this we can then calculate the conditional probabil-ity of a given category being rated highly within the testsegment by accounting for the change rate of rating prefer-ence for the category as follows:

Pr(+|c) =Prior Ratingz }| {Q

5

(c) +

Change Ratez }| {�

c

Q5

(c) (11)

Thereby, by averaging this over all categories for the itemi can can calculate the evolving item bias from the trainingsegment:

bi,cats(i)

=1

|cats(i)|X

c2cats(i)

Pr(+|c) (12)

@mrowebot m.rowe@lancaster.ac.uk

http://www.lancaster.ac.uk/staff/rowem/

Questions? 33

From Mining to Understanding: The Evolution of Social Web Users

Mining User Lifecycles from Online Community Platforms and their Application to Churn Prediction. M Rowe. International Conference on Data Mining. Dallas, US. (2013)

Changing with Time: Modelling and Detecting User Lifecycle Periods in Online Community Platforms. M Rowe. International Conference on Social Informatics. Kyoto, Japan (2013)