黃福銘 (Angus). Angus Fuming Huang Academia Sinica, Institute of Information Science, ANTS Lab Jae-Gil Lee Jiawei Han UIUC Kyu-Young Whang KAIST ACM SIGMOD’07

TMSG – Paper Reading黃福銘 (Angus)

2Angus Fuming

HuangAcademia Sinica, Institute of Information Science, ANTS Lab

Trajectory Clustering : A Partition-and-Group Framework

Jae-Gil Lee Jiawei Han

UIUC Kyu-Young

Whang KAIST

ACM SIGMOD’07

2012.01.04

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Paper outline

IntroductionTrajectory clusteringTrajectory partitioningLine segment clusteringExperimental evaluationDiscussion and conclusions

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1. Introduction

BackgroundThe key observationExamples in real applicationsPossible argumentsContributions

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Background

Previous research has mainly dealt with clustering of point data

K-means, BIRCH, DBSCAN, OPTICS, STING

Recent researches cluster trajectories as a whole

Improvements in satellites and tracking facilities

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The key observation

Clustering trajectories as a whole could not detect similar portions of the trajectories

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Examples in real applications

Hurricanes : landfall forecastsCoastline: at the time of landingSea: before landing

Animal movements : effects of roads and traffic

Road segmentsTraffic rate

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Possible arguments

If we prune the useless parts of trajectories and keep only the interesting ones

It is tricky to determine which part of the trajectories is useless

Pruning useless parts of trajectories forbids us to discover unexpected clustering results

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Contributions

Partition-and-group frameworkTo cluster trajectoriesTo discover common sub-trajectories

Formal trajectory partitioning algorithmMinimum description length principle

Density-based clustering algorithm for line segmentsDemonstrate by using various real data sets

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2. Trajectory clustering

Problem statementThe TRACLUS algorithmDistance function

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Problem statement

Input : a set of trajectoriesT = {TR1,…,TRnumtra

}

Output : a set of clustersO = {C1,…,Cnumclus

}

TrajectoryTri = p1p2p3…pj…pleni

Sub-trajectoryCharacteristic pointCluster

A set of trajectory partitions

Representative trajectoryThe major behavior of the trajectory partitions

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Example of trajectory clustering

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The TRACLUS algorithm

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Distance functionThe perpendicular distance ( d┴ )

The parallel distance ( d|| )

The angle distance ( dθ )

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3. Trajectory partitioning

Desirable propertiesFormalization using the MDL principleApproximate solution

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Desirable propertiesPreciseness

The difference between a trajectory and a set of its trajectory partitions should be as small as possible

ConcisenessThe number of trajectory partitions should be as small as possible

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Formalization using the MDL principle

To find the optimal tradeoff between preciseness and concisenessMinimum description length (MDL)

Cost components: H hypothesis; D data.L(H) is the length, in bits, of the description of the hypothesis; and L(D|H) is the length, in bits, of the description of the data when encoded with the help of the hypothesis.

Definition: The best hypothesis H to explain D is the one that minimizes the sum of L(H) and L(D|H).

A hypothesis corresponds to a specific set of trajectory partitionsFind the optimal partitioning translates to finding the best hypothesis using the MDL principle

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Formulation of the MDL costL(H) represents the sum of the length of all trajectory partitionsL(D|H) represents the sum of the difference between a trajectory and a set of its trajectory partitions

So~ Let’s minimize the L(H)+L(D|H)

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MDL=L(H)+L(D|H)

Approximate solution

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4. Line segment clustering

Density of line segmentsClustering algorithmRepresentative trajectory of a clusterHeuristic for parameter value selection

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Density of line segments

ε-neighborhood

Core line segment

Directly density-reachable

Density-reachable

Density-connected

Density-connected set

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Density-reachability and density-connectivity

L1, L2, L3, L4, and L5 are core line segmentsL2 (or L3) is directly density-reachable from L1L6 is density-reachable from L1, but not vice versaL1, L4, and L5 are all density-connected

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Influence of a very short line segment on clustering

A short line segment might induce over-clusteringOur experience indicates that increasing the length of trajectory partitions by 20~30% generally improves the clustering quality

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Line segments clustering algorithm

A cluster is a density-connected set

Trajectory cardinality

Be classified as a cluster or a noise

Directly density-reachable

ε-neighborhoodCore line segment

Cardinality checking

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Representative trajectory of a cluster

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Rotation of the X and Y axes

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Rep

rese

nta

tive tra

jecto

ry

gen

era

tion

alg

orith

m

3

5 6

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Heuristic for parameter value selection

The value of the ε and MinLnsSimulated annealingEntropy function

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5. Experimental evaluation

Experimental settingResults for hurricane track dataResults for animal movement dataEffects of parameter values

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Experimental setting

Hurricane track data setAtlantic1950~2004570 trajectories and 17736 pointsLatitude and longitude

Animal movement data setElk, 1993: 33 trajectories and 47204 pointsDeer 1995: 32 trajectories and 20065 points

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Clustering quality measurement

No well-defined measure for density-based clustering methodsSum of Squared Error (SSE)N : the set of all noise line segments

The noise penalty becomes larger if we select too small ε or too large MinLns

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Results for hurricane track data

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Results for animal movement data

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Effects of parameter values

Use smaller ε or larger MinLnsDiscovers a larger number of smaller clusters

Use a larger ε or a smaller MinLnsDiscovers a smaller number of larger clusters

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7. Discussion and conclusions

DiscussionConclusions

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Discussion

ExtensibilityUndirected or weighted trajectories

Parameter insensitivityPoint data, trajectory data

Efficiencyindex

Movement patternsCircular motion..

Temporal information

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Conclusions

Partition-and-group frameworkTrajectory clustering algorithm TRACLUSTwo real data sets experimentsA visual inspection toolCommon sub-trajectories

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My comments

Detailed sentence with explicit illustration !

What is the principle of the parallel distance function ? (p.14)What is the base for the 20~30% length increasing? (p.23)

Documents

黃福銘 (Angus). Angus Fuming Huang Academia Sinica, Institute of Information Science, ANTS Lab Jae-Gil Lee Jiawei Han UIUC Kyu-Young Whang KAIST ACM SIGMOD’07