Examining Activity Patterns Using Fuzzy Clustering

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Examining Activity Patterns Using Fuzzy Clustering

• by
• D De Silva, University of Calgary
• JD Hunt, University of Calgary
• PROCESSUS Second International Colloquium
• Toronto ON, Canada
• June 2005

2
Overview

• Introduction
• Data
• Method
• Preliminary Results
• Conclusions

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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

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Introduction

• Previous work
• Fair amount of work drawing in essence on three
  basic elements
• Data interpretation
• Similarity or Dissimilarity Measures
• Pattern Recognition Algorithms

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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 (PasWilson 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

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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

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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

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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)

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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

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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

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Method
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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

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Sequential Alignment Method

• 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

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Sequential Alignment Method

• 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)

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Sequential Alignment Method

• 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

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Sequential Alignment Method

• Output is a Dissimilarity Matrix

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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

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Fuzzy Clustering

• Minimize Objective Function (Kaufman)

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Fuzzy Clustering

• Number of clusters ?
• An Open question To be determined as part of
  research
• Two quality indices from S-Plus
• Dunns Coefficient
• Average Silhouette Value with Shadow plot

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Fuzzy Clustering

• Dunns Coefficient
• Where Fk always lies in the range 1/k,1.
•    ? entirely Fuzzy Clustering ?
• ? Crisp Clustering ?

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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
• 0lt - 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

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Cluster Center Interpretation

• 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

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Cluster Center Interpretation

• 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

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Results

• Sequential Alignment
• Low Vs High Gap Penalty Results
• Cluster plot for 3 clusters
• Low Gap High Gap

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Results

• Shadow Plot
• Low Gap High Gap

Co efficient Low Gap High Gap
Dunns Co-efficient 0.4 0.33
Average Silhouette Value 0.4 0.3

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

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Results

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

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Results

• Number of Clusters
• Potential range 2 to 5

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Results

• Number of Clusters (k)
• K2
• Fk 0.60 ASV 0.42

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Results

• Number of Clusters (k)
• K3
• Fk 0.43 ASV 0.40

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Results

• Number of Clusters (k)
• K 4
• Fk 0.34 ASV 0.32

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Results

• Number of Clusters (k)
• K 5
• Fk 0.28 ASV 0.20

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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
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• Fuzzy Cluster
• Memberships
• Output of S-plus software
• HH2701 has almost equal memberships to all three
  clusters -

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Results

• Fuzzy weighted frequency Distribution

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Results

• Cluster Interpretation

Crisp presentation
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Results

• Cluster 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 40s
• Majority Adults workers not needing a car to work
• Expect different for total sample

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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

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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

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Thank You

• ?