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**Incremental Clustering for Trajectories**

Zhenhui Li, Jae-Gil Lee, Xiaolei Li, Jiawei Han Univ. of Illinois at Urbana-Champaign DASFAA Conference 2010 April, Tsukuba, Japan

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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**Tracking by GPS/Sensor is becoming more common**

Vehicles Animals Hurricane

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**Moving object data is accumulated fast**

Taxi tracking system tracks 5,000 taxis in San Francisco Location information received each taxi every minute After a day, 7.2 million points collected After a week, 50.4 million points collected ...

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**Online monitoring demand**

Trajectory clusters have applications in discovering common hurricane paths monitoring hot traffic paths analyzing animals’ movement As data is updated along with time, there is need to online monitor the clustering result. But, it is inefficient to compute the trajectory clusters from scratch every time.

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**New data will only affect local shifts**

The key observation is that, the new data will only affect local shifts. Snapshot Time 1 Snapshot Time 2

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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**TRACLUS: trajectory clustering**

Clustering trajectories as a whole could not detect similar portions of the trajectories (i.e., common sub-trajectories) Example: if we cluster TR1~TR5 as a whole, we cannot discover the common behavior since they move to totally different directions Jae-Gil Lee, Jiawei Han, and Kyu-Young Whang, “Trajectory Clustering: A Partition-and- Group Framework”, in Proc ACM SIGMOD Int. Conf. on Management of Data (SIGMOD'07), Beijing, China, June 2007. A common sub-trajectory TR5 TR1 TR2 TR3 TR4

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**The Partition-and-Group Framework**

Consists of two phases: partitioning and grouping TR5 TR1 TR2 TR3 TR4 (1) Partition A set of trajectories A representative trajectory (2) Group A cluster A set of line segments Note: a representative trajectory is a common sub-trajectory

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Partition Identify the points where the behavior of a trajectory changes rapidly; such points are called characteristic points A trajectory is partitioned at every characteristic point A line segment between consecutive characteristic points is called a trajectory partition : characteristic point : trajectory partition

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**Group Group line segments based on density**

L1, L2, L3, L4, and L5 are core line segments L2 (or L3) is directly density-reachable from L1 L6 is density-reachable from L1, but not vice versa L1, L4, and L5 are all density-connected L1 L3 L5 L2 L4 L6 L L L L L L4 MinLns = 3

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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**TCMM Framework Trajectories received along with time**

Partition the trajectory into line segments A micro-cluster stores a small group of close line segments A macro-cluster a cluster of micro-clusters

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Data Preprocess Finding the optimal partitioning translates to finding the best hypothesis using the MDL principle H a set of trajectory partitions, D a trajectory L(H) the sum of the length of all trajectory partitions L(D|H) the sum of the difference between a trajectory and a set of its trajectory partitions L(H) measures conciseness; L(D|H) preciseness

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**Micro-Cluster Definition**

Micro-cluster maintains a fine-granularity clustering. Each micro-cluster holds and summarizes the information of local partitioned trajectories. A micro-cluster for a set of directed line segments is defined as the tuple: :number of line segments :linear sums of the line segments’ center points, angles and lengths :squared sums of the line segments’ center points, angles and lengths

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**Distance between Micro-Clusters**

Representative line segment of a micro-cluster Distance between two micro-clusters can be defined as the distance between representative line segments of two micro- clusters

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**Creating and updating Micro-Cluster**

When a new line segment is received Find the closest micro-cluster If the distance is between the new line segment and its closest micro-cluster is less than threshold , add the new line segment into this micro-cluster and update the micro-cluster If not, create a new micro-cluster, and the new micro-cluster only contains this line segment are the center, angle, and length of this line segment are the square of the center, angle and length of this line segment

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**Merging Micro-Clusters**

Why merging micro-clusters? If the number of micro-clusters is large, it is time-consuming to find the closest micro-cluster when a new line segment is received do macro-clustering over micro-clusters And the memory might not be enough to store all the micro- clusters Merge close micro-clusters to save storage space and save computation time “closeness” can be simply defined as the distance between two micro-clusters However, it does not consider the “tightness” of a micro-cluster

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**Merging Micro-Clusters (cont.)**

We prefer to merge loose micro-clusters rather than tight ones to better preserve the “tightness” of micro-clusters. Lose more information when merging two tight micro-clusters.

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**Merging Micro-Clusters (cont.)**

Introducing “extent” of a micro-cluster Extent defines the tightness of a micro-cluster in terms of center, angle and length

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**Merging Micro-Clusters (cont.)**

Distance between micro-clusters with extent Center distance Angle distance Length distance

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**Micro-clustering summary**

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Macro-Clustering Macro-clustering is evoked only when it is called upon by the user Macro-clustering is performed on the representative line segments of micro-clusters Similar to the group step in TRACLUS framework

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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Experiment Real taxi data in san Francisco, trajectories in a week, 100,000 points in total

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**Experiment (cont.) Effectiveness**

SSQ (sum of squared distance) is the average of all the line segments to the centroid of its macro-cluster TCMM reaches similar quality as TRACLUS

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Experiment (cont.) Efficiency TCMM is much faster than TRACLUS

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**Experiment (cont.) Sensitivity with parameter:**

When d_max is larger, the quality is lower but the efficiency is better

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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Conclusion We address the problem to incrementally cluster trajectories. We propose the TCMM (Trajectory Clustering based on Micro- and Macro-clustering) framework. The definition of extent is proposed to better capture the “tightness” of micro-clusters. Experiments show that TCMM achieves similar quality as TRACLUS but it is much faster.

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**Outline Motivation Introducing previous work TRACLUS**

Trajectory Clustering using Micro- and Macro-clustering Experiment Conclusion Future Work

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**Future Work Efficiency Parameter insensitivity Temporal information**

Use an index to find closest micro-cluster Not easy because our distance function is non-metric Parameter insensitivity Make our algorithm more insensitive to parameter values Temporal information Take account of temporal information during clustering Other applications Incrementally discover outliers and patterns

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Thank you!

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