Computations In Social Networks Sajid S Shaikh Advisor: Javed I Khan.

Computations In Social Networks

Sajid S Shaikh

Advisor: Javed I Khan

Structure Introduction

Related Work

Reputation Assessment System

Reputation Quantification System (RQS)

Reputation Reasoning System (RRS)

Reputation Based Social Computing

Social Network Based Computations

Classification

Examples

Conclusion

Introduction Internet is a virtual society.

Similar to a real society internet has a number of communities.

Communities are social knowledge reservoirs.

An assessment system is required to query the knowledge base.

P2P systems are the best examples of a community on internet.

Social Networking Websites (SNW) are latest P2P application.

Applied the assessment system to SNWs.

Orkut & LinkedIn

Network Members User Base

Orkut 22,000,000Designed specifically for friends and family.

LinkedIn 6,000,000Designed for professionals and adults.

MySpace 54,000,000Used mostly for fun and blogging.

Sporzoo 2,000,000Real Estate Investors and Professionals.

SelectedMinds 1,000,000Corporate social networking.

Reputation Assessment System Overview

The reputation assessment system consists of two components RQS : Derives reputation between directly connected nodes.

Generic reputation quantification function 4 canonical classes of the function with real life correspondence

• Fading Memory Averaging • Memory Less Summation • Fading Memory without Opinion Credibility• Memory Less Averaging

RRS : Derives reputation between dispersed nodes

Reputation based social computing

Related Work Gupta, Judge, and M. Ammar proposed system is specifically for peer-to-

peer systems. The system calculates the reputation based on variables which are specific to P2P systems and hence the system cannot be applied in other interaction based environments.

Damiani, Vimercati et.al. even though they incorporate community into their reputation function they do not take into consideration the credibility of the opinion.

Ecommerce websites such as eBay©, Yahoo© auction and Amazon© use a feedback based reputation system which is a simple memory less summation system .

Marti and Garcia-Molina propose a reputation system for a peer-to-peer environment, but their threat model only considers one class of attacks in which a malicious group is trying to work against the system. Their system is a simple voting system.

Reputation Assessment System Structure

Reputation Quantification System

Reputation Reasoning System

Notation

Reputation Quantification System

Estimates reputation

Any transaction consists of 3 sets Producer Product Consumer

With respect to reputation Producer: Opinion provider Product : Reputation Consumer : Individuals who use the

reputation to make decisions.

Opinion (O) & Time of Opinion (T)

R R

R

R

R

R

R

R

R RProduct

ConsumerProducer

Group Rating (W) & Number (N)


R R

R

R

R

R

R

R

R RProduct

ConsumerProducer



R R

R

R

R

R

R

R

R RProduct

ConsumerProducer



R R

R

R

R

R

R

R

R RProduct

ConsumerProducer


Social Factors Impacting Individuals Reputation

What does someone has to say about the individual – opinion

What is social standing of that someone – reputation

How long ago was this opinion expressed – age of opinion

How many people are saying something about the individual – number

What kind of group of people is expressing these opinions – group rating

All these factor not considered all the time some are omitted – impact

variable

Some may have more effect than others – impact weight

Generic Reputation Function (GRF) imp

Factors Influencing Reputation Computation Opinion (O) Reputation of Opinion Provider (R) Age of the Opinion (T) Number of Transactions (N) Group Reputation (W) Impact Parameters

Impact Variable (X) Impact Weight (α)

Stabilizing Factors Decay Rate (λ) Stable Value (Φ)

eeWN

eORWR jT

jWWNN

TXTj

OORR

m

j

N

j

TXX

N

j

TX

j

X

jm

k kAt

1 1

)(

1

)(

1

Different Scenarios

Are all variable (R,T,N,W) are valid in all scenarios ?

Table shows the 4 main scenario examples which have real life correspondence.

1110University ~ Students

0101University ~ Faculty

1110Automobile ~ Buyer

1111Automobile ~ Mechanic

1001Automobile ~ Manufacturer

1110Satellite ~ Satellite Service User

0101Satellite ~ Space Agency

1110Protocol ~ Users

1111Protocol ~ Companies

1111Course Material ~ Other Teachers

1001Course Material ~ Preparing Teachers

1110Course Material ~ Student

1111Article ~ Reader

0101Article ~ Journal

1001Article ~ Writer

0111Article ~ Reviewer

0111Movie ~ Critics

1110Movie ~ Viewers

1001Book ~ Author

1111Book ~ Reader

WNTRTarget ~ Evaluator

Canonical Classes of GRF GRF can be applied to different environments.

Every environment has different requirements.

Table shows the various real life combinations possible for the customizable variables

There are four broad classes of the GPF Fading Memory Averaging Memory Less Summation Fading Memory without Opinion Credibility Memory Less Averaging

Target ~ Evaluator R T N

Book ~ Reader 1 1 1

Book ~ Author 1 0 0

Movie ~ Viewers 0 1 1

Article ~ Journal 1 0 1

A Fading Memory Averaging Function

Valid Variables

Reader’s individual Reputation (R)

Reader’s opinion (O)

How fresh is the Opinion (T)

Number of Readers

nT

N

j

Tj

N

j

TjX

j

X

j

Ae

eeOR

RXTTOORR

t

1

)(

1

)(

)(


Book ~ Reader 1 1 1

A Memory Less Averaging Function

Valid Variables

Faculty’s Opinion (O)

Faculty’s Reputation (R)

Number of Opinions (N)

NeOR

RN

j

TjX

j

X

j

A

TOORR

t 1

)( 0

)(


University ~ Faculty 1 0 1

A Fading Memory Averaging Function without Opinion Credibility

Valid Variables

Viewer’s Opinion (O)

Age of Opinion (T)

Number of Opinions (N)

nT

N

j

Tj

N

j

TjX

jj

Ae

eeOR

RXTTOOR

t

1

)(

1

)(0

)(


Movie ~ Viewers 0 1 1

A Memory Less Summation Function

Valid Variables

Authors Opinions (O)

Authors Reputation (R)

NeOR

RN

j

TjX

j

X

j

A

TOORR

t0

0

)( 1

)(


Book ~ Author 1 0 0

Notation

Ei – Unique entity in super set E

Entities form various sets (A,B,C…)

Ei belongs to various sets.

AB denotes existence of relationship

between A & B.

Mr = A X B denotes relationship matrix

between the set members.

Mri – represents relationships of set A’s

members

MIj – represents relationships of B’s jth

member with all members of A

E1

E2

E4

E3

E

A BE4

Relationship Reasoning System Set of operations on relationship matrix M Relationship operations

Equivalence : M = N

Reflection : R = MT

Synthesis : S = M x N

Intersection : E = M ∩ N

Union : U = M U N

Exclusion : X = M θ N

Dediagonization :

Quantization :

Set Operations Column Extraction : (ψ)

Row Extraction : (ρ)

Max Row : (ξ)

Max Column : (Φ)

Zero Column :(θ)

M̂

M

Threats To Reputation Function

Attackers : Always lie Average Group

Good Group

Bad Group

Evaluators : Always honest

Target

Offender : Mostly honest but sometimes lies.

Reputation Attacks Classification

Attacks have been classified into 4 types

One – One Vendetta - Fight between two individuals

Many – One Gang Attack - A group working against an

individual

One – Many Dr Jekyll & Mr. Hyde - Dual behavior

Many – Many Mutual Boosting - Two-attacker groups join

together to mutually inflate reputations.

One Many

One Vendetta Dr Jekyll & Mr. Hyde

Many Gang Attack Mutual Boosting

Experimental Evaluation

Vendetta

Single target and single attacker

Attacker has random or high personal Reputation

Attacking frequency is random

Graphs - final Reputation against time of opinion

Personal attack has a very limited or no damaging effect

Fading Memory Averaging Function graphs

AT

TG

EV

EV

EV

Vendetta Graphs 1

0.97

0.15

0.97

0.520.99

0

0.2

0.4

0.6

0.8

1

1.2

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Evaluator Reputation

Attacker Opinion

Attacker Reputation

Final Reputation

Evaluator Opinion

Evaluator Reputation High

Evaluator Opinion Random

Attacker Reputation High

Attacker Opinion Low

Behavior of Reputation function when Attacker and Evaluators have high personal reputation

Attack Period

Vendetta Graphs 2

Evaluator Reputation Random

Evaluator Opinion High

Attacker Reputation Random


Behavior of Reputation function when Attacker has low reputation and evaluators have random reputation

0.96

0.76

0.39

0.40

0.19

0

0.2

0.4

0.6

0.8

1

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Evaluator Opinion

EvaluatorReputation

Final Reputation

Attacker Opinion

AttackerReputation

Attack Period

Gang Attack

Group attacking a single target

Attack group has random or high personal Reputations.

Attackers manage to bring down the reputation.

But no permanent damage.

Function recovers itself.

Fading Memory Averaging Function graphs

AT

AT

AT

TGEV

EV

EV

Gang Attack Graph 1

0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109

0.05

0.25

0.45

0.65

0.85

1.05

1.25

1.45

1.65

1.85 Evaluator Reputation

Attacker Opinion

Attacker Reputation

Final Reputation

Evaluator Opinion



Attacker Reputation High


Behavior of reputation function when attackers and evaluators have high reputation

Attack Period

Gang Attack Graph 2

0.91

0.74

0.12

0.69

0.97

0

0.2

0.4

0.6

0.8

1

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 Evaluator Opinion

AttackerReputation

Attacker Opinion

Final Reputation

EvaluatorReputation



Attacker Reputation Random


Behavior of reputation function when attacker has random reputation and evaluators have high reputation

Attack Period

Dr. Jekyll & Mr. Hyde Dual conflicting behavior of a peer. The peer develops a high reputation, then misbehaves Evaluator group penalizes him. Peer’s reputation goes down. Recovers back to original value if peer indulges in honest

transactions.

AT

TG

TG

TG

Dr Jekyll & Mr. Hyde Graph 1

0.11

0.74

0.9

0

0.2

0.4

0.6

0.8

1

1.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

EvaluatorOpinion

FinalReputation

EvaluatorReputation


Normal period Evaluator Opinion High

Penalty period Evaluator Opinion Low

Behavior of reputation function when evaluators have high reputation

Penalty Period

Dr Jekyll & Mr. Hyde Graph 2Behavior of reputation function when evaluators have random reputation

Evaluator Reputation Random

Normal period Evaluator Opinion High

Penalty period Evaluator Opinion Low

0

0.2

0.4

0.6

0.8

1

1.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77

EvaluatorOpinion

EvaluatorReputation

FinalReputation

Penalty Period

Mutual Boosting

Groups intentionally give high opinion to each other

High reputed group’s reputation drops

Low reputed group’s reputation rises

Eventually all the groups have same reputation.G1

G1 G1

G1 G1

G2

G2 G2

G2 G2

Mutual Boosting GraphBehavior of reputation function when one group has high reputation, one has average reputation and one has low reputation members

Reputation Opinion

Member Group 1 High High

Member Group 2 Average High

Member Group3 Low High

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10

MEMBER 0

MEMBER 1

MEMBER 2

Social Network Based Computations

Social Profile Mining

Social Fabric Analysis

Social Linkage Analysis

Social Ranking Analysis

Placement Within a Community

A B C D


A B

C

D


A B

C

D


A B

C

D


A B C D


A B C D


A B

C

D


A B

C

D


A B

C

D


A B

C

D


A B

C

D


A B

C

D


Social Profile Mining Definition : The process of searching large volumes of data for hidden patterns, to

predict future behavior

Uses: Geo-Profiling, Demographic information, Market Analysis.

SNW are a rich database of individual’s personal and professional information.

This data can be subjected to descriptive and inferential statistical analysis.

Descriptive: Mean, Mode & Standard Deviation

Inferential: Hypothesis testing, Estimation, Correlation, Regression.

Examples: Mining the cuisine and favorite movie sections of Orkut


Definition: Given a weighted graph G(V,E), and given further one element v of V, find the strength of social property S on v for each v’ of V.

Social Fabric analysis derives social properties using primary relationships.

Primary relationships: father, mother, friend etc

Social properties: Influence, status, reputation, trust.

Example: Influence Propagation

Influence

Definition:” the act or power of producing an effect without apparent exertion of force or direct exercise of command”

Factors affecting influence: I-factors

Age Difference (F1)

Age determined from profile on SNW

Proximity of Nodes (F2)

City , State and Country determined from SNW profile

Relationship Type (F3)

Monitoring Interactions

Contact Frequency (F4)

Interaction Monitoring

jicountryjistatejicityfjiF .,,,,,

2

i,jjiF Relation,3

N

jiji

NkF

,scrap, 1

4

ageageF jiji

,1

Influence Context (F5)

Influencing node’s Reputation (F6)

Using RQS

Trust (F7)

Using RQS

Influence (I)

Tn

N

j

Tj

N

j

TjX RR

j

X

j ee

eORF

XTTOO

A

1

)(

1

)(

6

Tn

N

m

mT

N

m

TjX

mX

ie

eeKRF

XTTOORR

ji

1

)(

1

)(

7,

7654321 ,,,,,, FFFFFFFfI

Influence: Algorithmic Structure

Depth first traversal of network

Go to next node if relationship link

part of favorable links

Next node should satisfy I-factors to

continue traversal

Traversal length dependant on

relationship chain

Mostly 3 hops

Time complexity is O(|v| + |e|)

Influence (G, u, δ, λ) u - is the source node

Stack S = { };

Stack O = { };

Boolean x, y;

pathString (u) = null;

Push S, u;

while ( S is not empty ) do

u := Pop S;

Push S, u;

for each vertex v adjacent to u

if ( AgeV > 18 ) && ( F1(u, v) > 2) && ( F6(v) > δ) && (F7(u, v) > λ )

I = (AgeV /100) * (F1 (u, v)/50) * F6 (v) * F7 (u, v);

pathString(v) = Concatenate ( pathString(u), F3(u,v));

Push S, v;

StringMatching(pathString(v), patternDb())

I = I * patternDb(pathString(v)).value();

return I;

end if

end while

Influence Derivation

Peter

George

Bob

Laura

Kallis

JoeMartin

Friend

Spouse

Father

Coworker

Friend

Neighbor

Scraps

City, State, Country

Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Peter

George

Bob

Laura

Kallis

JoeMartin

Friend

Spouse

Father

Coworker

Friend

Neighbor

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

George’s Social Network On Orkut

George

D

M

K

J

H

G

B

I

A

Y

L

N

ZN

Peter

George

Bob

Laura

Kallis

JoeMartin

Spouse

Father

Coworker

Friend

Neighbor

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

0.9

0.9

0.5

0.2

0.50.20.4

0.7

0.02

0.1

Peter

George

Bob

Laura

Kallis

JoeMartin

Spouse

Father

Coworker

Friend

Neighbor

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

Scraps


Age

0.9

0.9

0.5

0.2

0.50.20.4

0.7

0.02

0.1

Numbers indicate F7 values


Definition: Given a graph G(V,E) , where each edge u,v denotes a relationship r(u,v), we want to find the most effective relationship chain from source s to the sink t subject to certain constraints

Source “s” and Sink “t” are fixed

Determine the relationship chain that maximizes probability of contact between s and t

Example : Vested Socialite

Vested Socialite

Definition:” A person trying to force himself into other people’s social

network in order to achieve some objective”

Factors for social insertion: V-factors

Objective

Constraining factors

Direct influence

Derived influence

Relationship chain

Hate list

Vested Socialite : Algorithmic Structure

Determine path from s to t

Drop path if it contains hate list member

Drop path if it violates constraints.

If more than 1 path , chose the one with

highest contact probability

Some favorable relationship chains:

Friend{1,}

Friend-Relative-Friend

Relative-Friend{1,2}

Relative-Friend-Relative

Coworker-Friend,

Coworker-Relative

FindPath(G, start, t, path)

Array paths;

Concatenate (path, start)

If start == end

return path

for each node n in G

if(StringCompare(F3(start, n), Enemy)) == false

if n not in path

newpath=FindPath(G, n, t, path)

paths.add(newpath)

end if

end if

return paths[ ];

InsertProbabilty(paths[ ], start, t)

for each path p in paths

for each node n in path p

rchain(p) = rchain(p) + F3(n, n+1)

StringMatch(rchain(p), patternDb())

if true then

insertprobability = patternDb(relationchain(p)).value();

return insertprobabilty;

break;

Vested Socialite

John

Victor

Gary

DavidSteven

Paul Raj

Frank

John

Victor

Gary

DavidSteven

Paul Raj

Frank

John is “s” and Victor is “t”

John

Victor

Gary Steven David Frank

Paul Raj

ENEMY

SUBORDINATE

FRIEND

FATHER

FATHER

BOSS

FATHER

FRIEND

FRIEND

FRIENDFRIEND

John

Victor

Gary

DavidSteven

Paul Raj

Frank

Father

Friend

Enemy

Friend

Father

Subordinate

FatherBoss

Friend

Friend

Friend

John

Victor

Gary

DavidSteven

Paul Raj

Frank

Father

Friend

Enemy

Friend

Father

Subordinate

FatherBoss

Friend

Friend

Friend

Favorable paths in blue. Unfavorable in red


Definition: Given a graph G(V,E), we want to determine the ranking of all v

of V based on a social property P.

Ranking algorithms are used while making decisions

Ranking changes with social property.

Example: Ranking based on Trust

Trust Based Ranking

Two groups are considered

Sink ranking group Nodes that trust the target “t”

Source ranking group Nodes the target “t” trusts

Final ranking is combination of source and sink rankings.

j1

i

j4

j3j2

Tj1i

Tj2iTj3i

Tj4i

j1

i

j4

j3j2

Tj1i

Tj2iTj3i

Tj4i

j1

i

j4

j3j2

Tij1

Tij2Tij3

Tij4

j1

i

j4

j3j2

Tij1

Tij2Tij3

Tij4

Algorithm: Eigen Computation

Sink ranking

Source ranking

Generalized Equation

λ is an eigenvalue of T.

The eigenvalue determines the eigenvectors.

The eigenvectors represent the rankings.

Eigenvalue and eigenvector computation require O(n3) operations

xTx ji

n

jji

1

1

xTy jiji

n

j

T

1

1

xxTTT

Community Placement

Definition: Community placement is the problem of finding highly connected individuals within a community who could influence a majority of the community to agree on or believe in an issue.

Propagandist use a brute force method – meeting every individual

Better approach is to influence a coterie

Extension of social ranking with the extra task of finding the appropriate individuals.

Multi-Faith Group

Gather a group of individuals from varied faiths and use them to propagate religious tolerance.

The individuals should satisfy the following conditions Should be from different faiths Should be highly connected Should have friends belonging to different faiths.

Multi-Faith Group: Algorithm

Two main stages: ranking and propagation

Ranking algorithm finds everyone’s ranking.

Top ranked individual sends agenda to his neighbors and the influencing power is recorded.

He is then pruned from the graph.

The above step is repeated until a majority is influenced

Time complexity would be O(n3) + O(|V|+|E|)

Conclusion

We have presented a framework to represent and reason with

general case of social relationship network in a formal way.

We have provided an assessment system using which the

strength of relationship can be measured.

We provide a classification for the potential applications of the

rich database that users of social networking websites are

unknowingly creating and further enriching everyday.

The application classifications are substantiated by providing

complex examples for each class.

References

Gupta, M., Judge, P., and Ammar, M.,( 2003) "A reputation system for peer-to-peer networks" in NOSSDAV. pp 144 -152

Damiani, E., De Capitani di Vimercati, S., Paraboschi, S.,and Samarati, P., (2003)“Managing and sharing servants’’ reputations in P2P systems”. IEEE Transactions on Data and Knowledge Engineering.pp 840–854.

Marti, S., and Garcia-Molina, H.,(2004). “Limited reputation sharing in P2P systems”. In Proc. of the 5th ACM conference on Electronic commerce, New York, NY, USA, pp 91-101,

Gambetta, D., (1988) “Trust making and breaking cooperative relations”. New York: Blackwell

McKnight, D., & Chervany, N., (1996) “The Meaning of Trust”. University of Minnesota MIS Research Center Working Paper Series, WP 96-104

McShane, S., (1995). Canadian Organization Behavior. Ottawa:Irwin. Meneses, J., (2004) “The Orkut.com case: a reflection on the exploration of new ways

to online sociability in the tradition of the study of virtual communities”. Xiong, L., and Liu, L.,. (2003). “A reputation-based trust model for peer-to-peer

ecommerce communities”. IEEE Conference on E-Commerce (CEC'03). pp 275 – 281

Malaga., R. A., (2001.). “Web-based reputation management systems: Problems and suggested solutions”. Electronic Commerce Research. pp 403 – 417

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Computations In Social Networks Sajid S Shaikh Advisor: Javed I Khan.

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Transcript of Computations In Social Networks Sajid S Shaikh Advisor: Javed I Khan.