Examining Activity Patterns Using Fuzzy Clustering by D De Silva, University of Calgary JD Hunt,...

Examining Activity Patterns Using Fuzzy

Clusteringby

D De Silva, University of CalgaryJD Hunt, University of Calgary

PROCESSUS Second International Colloquium

Toronto ON, CanadaJune 2005

Overview• Introduction

• Data

• Method

• Preliminary Results

• Conclusions

Introduction• Context

• Activity-based transport models increasing• Need for grouping into segments• At present seems largely based on received

wisdom

• Motivations

• Opportunity in Calgary• Large Household Activity Diary Survey• Interest in Activity-based model development• Willingness to explore issue of grouping

• Increase understanding of activity patterns resulting from behavioral processes

Introduction

• Previous work

• Fair amount of work drawing in essence on three basic elements

• Data interpretation

• Similarity or Dissimilarity Measures

• Pattern Recognition Algorithms

Introduction• Previous work (Contd.)

• Data Interpretation• Some used Time Slices in 5 to 15 minute intervals

(Recker et al; Wilson)• Others Disagreed with it and used number of stops

made. (Pas)

• Similarity or Dissimilarity Measures• Similarity Matrix (Pas;Wilson; Ma)

• Sequential Alignment Method (Wilson; Jun Ma)• Walsh-Hadamand transformation, a Fourier Type

Analysis, (Recker et al)

• Pattern Recognition Algorithms• All have used Crisp Clustering Methods

Introduction• Previous work (Contd.)

• Groups with similar activities• Pas – 12 groups based on the number of non-home stops• Recker – 7 Groups based on Socio Economic Data• Wilson – 8 groups Similar to Recker

• Applications• To Model Inter Shopping Duration (Bhat)• Micro simulation of Activity Patterns (Kitamura et al;

Kulkarni et al)

• Extension – the work described here• Time Slices• Sequential Alignment Method• Fuzzy Clustering

DataHousehold Activity Survey

(HAS)• 24-hour diary• Fall of 2001• Sample size

• 8,400 households overall• 5,900 on weekdays

• 15-minute intervals• activity• location

• Activities in 19 categories• Locations

• X,Y• Home, Work , Travel, Other

• All household members

Activities Covered in HAS

• Travel (A)• Pick Up Someone (B)• Drop Off Someone

(C)• Work (D)• School / Homework

(E)• Shopping (F)• Daycare (G)• Social (H)• Eating (J)

• Entertainment / Leisure (K)

• Medical / Financial (L)• Exercise (M)• Religious / Civic (N)• Sleeping (O) • Household Chores (P)• Park / Un-park Vehicle (X)• Work-Travel(e.g. Taxi Driver) (Y)• Out-of-Town (Z)

Example Sequence

• Activity Sequence of • 30 min Sleep• 15 min Eat • 30 min Travel• 1 hr Work

• O O J A A D D D D

Initial Sample for Testing

• Covered in this presentation • 75 persons• 50 households• Just activity type and weekdays (not

location & weekends)

• Later consider:• Full sample• Weekends and weekdays• Location types as a further dimension

Method

Dissimilarity Matrix

Groups of Similar Activity Patterns

Sequential Alignment Method

(CLUSTALG Software)

Data Set (Time Slices)

Fuzzy Cluster Memberships

Fuzzy Clustering(S-Plus

Software)

Cluster Center Interpretation

•Socio Economic Variable Distribution•Fuzzy Weighted Frequency Distributions

Sequential Alignment Method (SAM)

• Alignment Methods first used in field of Molecular Biology for DNA matching

• Activity Travel Patterns Intrinsically Sequential

• SAM Evaluation of Sequence of Characters• Global Alignment (Whole Sequence)• Local Alignment (Short sequence within entire

sequence)

• Simplest case is Pairwise alignment


• Pairwise Alignment• Two Character Sequences

• ID 1: O O J A A D D D D• ID 2: O O O J A D D D O

• Elementary Operations until equal• Insertions and Deletions (Indel)• Gaps

• Gap insertion and extension Penalties

• Global Alignment – Needleman & Wunch algorithm minimizing the distance or maximizing the similarity

• ID 1: - O O J A A D D D D -• ID 2: O O O J A - D D D – O• Similarity Score = 70

• Lesser operations Similar Pair

• Gap Opening and Extension Penalties• Role of gap penalty• High Value

• Alignment compressed• Literally to matches avoiding gaping• Resemble main activities at their relative times• Recommended values 8 and 3 (Wilson)

• Low Value• Identification of similar activities displaced during the

day• Better pairwise comparison• Little similarity to the actual activity Pattern• Recommended values 1 and 0.1 (Wilson)

• Tested and accepted recommendation of Low Value for Transportation Research (Wilson)


• Multiple Alignment

• Extension of pairwise alignment to N dimensions

• Computation power enormous after 10 sequences of reasonable length

• Approximation method based on data of pairwise alignment

• Use of ClustalG software by Wilson



• Output is a Dissimilarity Matrix

HH4104 HH4904 HH503 HH401 HH2103 HH2401

HH4104 0

HH4904 0.122 0

HH503 0.148 0.165 0

HH401 0.574 0.523 0.533 0

HH2103 0.553 0.5 0.511 0.224 0

HH2401 0.419 0.393 0.407 0.153 0.123 0

Fuzzy Clustering• Partition Clustering Method • Number of clusters k - specified in front• The Objects (Activity Patterns) are not

assigned to a particular cluster but assigned a membership ranging between 0 and 1 for all clusters

• Uses S-plus Software (Kaufman Procedure)

• Dissimilarity matrix is input

Fuzzy Clustering• Minimize Objective Function

(Kaufman)

cluster v object to of iMembership u

ElementMatrixityDissimilarjid

where

u

jiduu

thth

k

v ivu

k

vn

j jv

n

ji jviv

iv

…1, = ifor 1

1

k. ..,…1, = vandn ,…1, = ifor 0 ivu

11

2

1,

22

),(

n.,

2

),(

Fuzzy Clustering

• Number of clusters ?

• An Open question – To be determined as part of research

• Two quality indices from S-Plus

• Dunn’s Coefficient • Average Silhouette Value with Shadow plot

Fuzzy Clustering

• Dunn’s Coefficient

Where Fk always lies in the range [1/k,1].

• entirely Fuzzy Clustering

• Crisp Clustering

n

i

k

v

ivk n

uF

1 1

2

kFk

1 k

uiv

1

1or 0ivu1kF

Fuzzy Clustering• Average Silhouette Value (ASV) with Shadow plot

• Strength of Classification to the nearest crisp cluster compared to the next best cluster

• Width of Bar• 1 – Well Classified• 0 – Between two clusters• 0< - Badly classified (lies near the next best

cluster)

• Average Value gives a approximation to the best number of clusters

• ASV must be higher than 0.25

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Silhouette width

Average silhouette width : 0.4


• Distributions of socio-economic variables• Basis for grouping in subsequent modeling• Person characteristics:

• Age• Gender• Person type category from survey• Employment Status

• Household characteristics: attributed to persons• Only income so far• Household structure later

• Fuzzy weighted frequency distributions

• Need for eventual Crisp

• Potentially use logit to assign cluster membership values • Calibrate ‘utility functions’ for clusters with person

characteristics• Use Monte Carlo to select specific cluster in each case


• Fuzzy Weighted Frequency Distributions;

• Bar for category in histogram for cluster is Percentage sum of people for that category in entire sample factored by cluster membership

M F M F M F

HH1503 0.4665 0.3907 0.1428 F 0 0.4665 0 0.3907 0 0.1428

HH1504 0.4618 0.3587 0.1795 F 0 0.4618 0 0.3587 0 0.1795

HH1801 0.4511 0.3094 0.2395 M 0.4511 0 0.3094 0 0.2395 0

HH2102 0.4197 0.3927 0.1876 M 0.4197 0 0.3927 0 0.1876 0

HH2503 0.5391 0.3234 0.1375 M 0.5391 0 0.3234 0 0.1375 0

HH2504 0.5208 0.3346 0.1447 M 0.5208 0 0.3346 0 0.1447 0

2.8590 2.1095 1.0315 1.9307 0.9283 1.3601 0.7494 0.7092 0.3223

68% 32% 64% 36% 69% 31%

Individual ID

Cluster Membership

Gender Cluster 1 Cluster 2 Cluster 3

Fuzzy Gender Distribution

C1 C2 C3 Fuzzy Weighted Frequency Distribution

0%

20%

40%

60%

80%

M F

Cluster 1

Cluster 2

Cluster 3

Results

• Sequential Alignment• Low Vs High Gap Penalty Results

• Cluster plot for 3 clusters

Low Gap High Gap

Component 1

Com

pone

nt 2

-0.4 -0.2 0.0 0.2

-0.4

-0.2

0.0

0.2

These two components explain 40.11 % of the point variability.Component 1

Com

pone

nt 2

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

These two components explain 33.75 % of the point variability.

Results

• Use low Gap Penalty – consistent with recommendation (1 and .1)

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Silhouette width


• Shadow PlotLow Gap High Gap

0.0 0.2 0.4 0.6 0.8 1.0

Silhouette width


Co efficient Low Gap High Gap

Dunn’s Co-efficient 0.4 0.33

Average Silhouette Value

0.4 0.3

Results

• Number of Clusters

• Clustal Plot Helps to See the potential range of number of clusters for Clustering

0.1

HH2701

HH503

HH4104

HH4904

HH505

HH905

HH2503

HH504

HH3603

HH903HH904HH4103

HH2504

HH3002HH3003

HH3703

HH4003

HH4903

HH3101HH3702

HH506

HH4004

HH3902

HH4602HH1603

HH3402HH802HH803

HH1901

HH4701

HH1502

HH2402

HH1504

HH3706

HH3403

HH603 HH3704HH3705HH1503

HH3903HH1801HH2102

HH501

HH601

HH902

HH2401

HH401

HH2103

HH3401HH403

HH3602

HH502HH901

HH3001HH1604

HH1601

HH1602

HH4101HH602

HH3601

HH2501

HH2502

HH4901

HH402

HH3701

HH1501

HH1902HH801HH4601

HH4001HH4002HH4102HH3901HH4902

HH2101

Results

• Number of Clusters

• Potential range 2 to 5

0.1

HH2701

HH503

HH4104

HH4904

HH505

HH905

HH2503

HH504

HH3603

HH903HH904HH4103

HH2504

HH3002HH3003

HH3703

HH4003

HH4903

HH3101HH3702

HH506

HH4004

HH3902

HH4602HH1603

HH3402HH802HH803

HH1901

HH4701

HH1502

HH2402

HH1504

HH3706

HH3403

HH603 HH3704HH3705HH1503

HH3903HH1801HH2102

HH501

HH601

HH902

HH2401

HH401

HH2103

HH3401HH403

HH3602

HH502HH901

HH3001HH1604

HH1601

HH1602

HH4101HH602

HH3601

HH2501

HH2502

HH4901

HH402

HH3701

HH1501

HH1902HH801HH4601

HH4001HH4002HH4102HH3901HH4902

HH2101

Results• Number of Clusters (k)

• K=2

• Fk = 0.60 ASV = 0.42

Component 1

Com

po

nen

t 2

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

0.4


0.0 0.2 0.4 0.6 0.8 1.0

Silhouette width



• K=3

• Fk = 0.43 ASV = 0.40

Component 1

Co

mp

on

ent

2

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2


-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Silhouette width



• K= 4

• Fk = 0.34 ASV = 0.32

Component 1

Co

mp

on

en

t 2

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2


-0.5 0.0 0.5 1.0

Silhouette width



• K= 5

• Fk = 0.28 ASV = 0.20

Component 1

Com

po

nen

t 2

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2


-0.5 0.0 0.5 1.0

Silhouette width


Results• Number of Clusters (k) ?

• Use 3 clusters for testing

• Expect different for total sample

2 Clusters

3 Clusters

4 Clusters

5 Clusters

Fk 0.60 0.43 0.34 0.28

ASV 0.42 0.40 0.32 0.20

Fuzzy Cluster Memberships

• Output of S-plus software

• HH2701 has almost equal memberships to all three clusters -

Person ID

Crisp Cluster C1 C2 C3

Person ID

Crisp Cluster C1 C2 C3

HH1501 3 0.1118 0.1145 0.7737 HH3902 2 0.3065 0.5194 0.1741HH1502 2 0.3406 0.4965 0.1628 HH3903 1 0.4534 0.4175 0.1291HH1503 1 0.4665 0.3907 0.1428 HH4001 3 0.1598 0.1669 0.6732HH1504 1 0.4618 0.3587 0.1795 HH4002 3 0.1311 0.1343 0.7346HH1601 3 0.2210 0.2055 0.5735 HH4003 1 0.4774 0.3300 0.1925HH1602 3 0.2728 0.2597 0.4675 HH4004 2 0.3372 0.4198 0.2431HH1603 2 0.2940 0.5723 0.1338 HH401 3 0.2625 0.2978 0.4396HH1604 3 0.2752 0.2475 0.4773 HH402 3 0.2372 0.2238 0.5390HH1801 1 0.4511 0.3094 0.2395 HH403 3 0.0236 0.0266 0.9498HH1901 2 0.3366 0.4470 0.2164 HH4101 3 0.2425 0.2451 0.5124HH1902 3 0.1838 0.1768 0.6394 HH4102 3 0.0689 0.0699 0.8611HH2101 3 0.1804 0.1883 0.6313 HH4103 1 0.5112 0.3297 0.1591HH2102 1 0.4197 0.3927 0.1876 HH4104 1 0.4189 0.3856 0.1955HH2103 3 0.2423 0.2359 0.5218 HH4601 3 0.1783 0.1897 0.6321HH2401 3 0.2132 0.2344 0.5524 HH4602 2 0.2625 0.5847 0.1528HH2402 2 0.3368 0.5158 0.1474 HH4701 2 0.3343 0.5097 0.1560HH2501 3 0.1228 0.1401 0.7372 HH4901 3 0.1349 0.1447 0.7205HH2502 3 0.2253 0.2470 0.5277 HH4902 3 0.1452 0.1658 0.6890HH2503 1 0.5391 0.3234 0.1375 HH4903 1 0.5106 0.3130 0.1763HH2504 1 0.5208 0.3346 0.1447 HH4904 2 0.3916 0.4309 0.1775HH2701 2 0.3407 0.3412 0.3181 HH501 2 0.3251 0.3753 0.2996HH3001 3 0.2563 0.2346 0.5092 HH502 3 0.2047 0.2015 0.5938HH3002 1 0.5152 0.3272 0.1577 HH503 1 0.3978 0.3601 0.2421HH3003 1 0.5384 0.3078 0.1538 HH504 1 0.5740 0.3004 0.1256HH3101 2 0.3258 0.4150 0.2592 HH505 1 0.3750 0.3435 0.2815HH3401 3 0.1330 0.1351 0.7319 HH506 2 0.3758 0.4553 0.1689HH3402 2 0.3073 0.5744 0.1183 HH601 2 0.2976 0.3905 0.3120HH3403 1 0.4152 0.3697 0.2150 HH602 3 0.1633 0.1670 0.6697HH3601 3 0.2416 0.2391 0.5194 HH603 2 0.3796 0.3873 0.2331HH3602 3 0.2240 0.2061 0.5698 HH801 3 0.1589 0.1695 0.6715HH3603 1 0.4916 0.3428 0.1656 HH802 2 0.2771 0.6039 0.1190HH3701 3 0.1898 0.1805 0.6297 HH803 2 0.2771 0.6039 0.1190HH3702 2 0.3656 0.4784 0.1560 HH901 3 0.2316 0.2277 0.5406HH3703 1 0.4717 0.3396 0.1886 HH902 3 0.2047 0.2205 0.5748HH3704 1 0.4291 0.3709 0.2000 HH903 1 0.4616 0.3467 0.1918HH3705 1 0.4291 0.3709 0.2000 HH904 1 0.6005 0.3023 0.0973HH3706 1 0.3972 0.3268 0.2760 HH905 1 0.5167 0.3764 0.1069HH3901 3 0.1108 0.1125 0.7767

ResultsFuzzy weighted frequency Distribution

Gender Distribution

0%

10%

20%

30%

40%

50%

60%

70%

80%

M F

Gender

Cluster 1Cluster 2Clluster 3

Age Distribution

0%

5%

10%

15%

20%

25%

30%

0 -

56

- 10

11 -

15

16 -

20

21 -

25

26 -

30

31 -

35

36 -

40

41 -

45

46 -

50

51 -

55

56 -

60

61 -

65

66 -

70

71 -

75

>75

Age

Pe

rce

nta

ge

(%

)

Cluster 1

Cluster 2Cluster 3

Person Category Distribution

0%

10%

20%

30%

40%

50%

60%

70%

KEJ

S

SH

S

PSS

AW

NN

C

AW

NC

AO

Sen YO

Person Category

Pe

rce

nta

ge

(%

)

Cluster 1

Cluster 2

Cluster 3

Age Distribution

0%

5%

10%

15%

20%

25%

30%

0 -

56

- 10

11 -

15

16 -

20

21 -

25

26 -

30

31 -

35

36 -

40

41 -

45

46 -

50

51 -

55

56 -

60

61 -

65

66 -

70

71 -

75

>75

Age

Pe

rce

nta

ge

(%

)

Cluster 1

Cluster 2

Cluster 3

Employment Status

0%

10%

20%

30%

40%

50%

60%

70%

80%

Emp

Self_E

mp

Un_Em

pl

Retrd

Home_

MVolu

nStu

dt

Employment Status

Pe

rce

nta

ge

(%

)

Cluster 1

Cluster 2

Cluster 3

ResultsCluster Interpretation

Annual Houshold Income

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Refused

25000-35000

45000-55000

65000-75000

100000-125000

>150000

Annual Household Income ( Cad $)

Pe

rce

nta

ge

(%

)

Cluster 1

Cluster 2

Cluster 3

Cluster 1 Cluster 2 Cluster 3

Male 64% 21% 61%Female 36% 79% 39%

KEJS 56% 0% 0%SHS 0% 5% 0%PSS 8% 5% 0%AWNNC 4% 11% 90%AWNC 0% 16% 10%AO 0% 21% 0%Sen 4% 26% 0%YO 28% 16% 0%

Employed 4% 18% 90%Self Employed 0% 12% 6%Unemployed 0% 0% 0%Retired 0% 12% 3%Homemaker 4% 18% 0%Volunteer 0% 24% 0%Student 92% 18% 0%

12 39 39%Avg. Age

Parameter

Gender

Person Type

Employment Status

Crisp presentation

ResultsCluster Interpretation - tends to be more;

• Cluster 1• Students age of 5 to 15• Mainly KEJS and youths

• Cluster 2• Females• Seniors and other adults in Age range 66-70• Retired home makers and volunteers

• Cluster 3• Males• 100% Adults workers • Age 40’s• Majority Adults workers not needing a car to work

• Expect different for total sample

Conclusions

• Methods seems to work well to identify the clusters as intended – no hurdles.

• Fuzzy clustering better indicate strength of membership

• Best to have multiple measures “quality” of clustering regarding number of clusters

• Still work in progress• Results not complete – just for example

• But essential elements of analysis process set

Conclusions

• Future Work

• Proceeding to full sample of 8,400 households including Weekends

• Expanding to location dimension

• Calibrate Logit model for allocation of clusters

• Consider Household Structure

Thank You?

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