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Learning Trajectory Patterns by Clustering: Comparative Evaluation Group D

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Problem Description & Definition

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Preprocessing Grid Quantization Clustering Distance/Similarity - modified Euclidean distance, dynamic time warping and longest common sequence Clustering - bisection, Agglomerative and min-cut graph based with number of clusters predefined Clustering Validation Ground-truth based Hungarian Algorithm for matching clusters generated with ground-truth clusters Problem Description & Definition

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Preprocessing Grid quantization s=2 Normalization Grid Quantization

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Preprocessing Location 1 Location 2 Location 3 Location 4 Computation Complexity Reduction Entry and Exit detection based on clustering starting and ending points of each trajectory (k-means clustering k=4)

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Distance Metrics Modified Euclidean Distance (m>n) Dynamic Time Warping DTW is used to compare unequal length signals by ﬁnding a time warping that minimizes the total distance between matching points

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Distance Metrics Longest Common Sub Sequence s 1 ={a, b, c, d, e, f}; s 2 ={b, d, e, f, m,n} LCSS(s 1,s 2 )={b, d, f} where δ is a constant that controls how far we can look in the past and ε is a constant that controls the size of proximity in which we are looking for matches

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Gaussian Kernel Function Distance to Similarity Metrics A similarity matrix S = {sij}, which represents a fully connected graph, is constructed from the trajectory distances using a Gaussian kernel function Where D represents one of the distance measure deﬁned previously and the parameter σ describes the trajectory neighborhood. Large values of σ cause further apart trajectories to have a higher similarity score while small values lead to a more sparse similarity matrix (more entries will be very small) σ =0.1σ =0.9σ =2.1σ =4.1 σ =7.1 DTW

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Clustering Methods(CLUTO) Divisive Divisive clustering is the top-down clustering where the entire trajectory training set is considered a single cluster. The K clusters are obtained by performing K − 1 repeated bisections where each bisecting cluster split results an optimal 2-way division of the similarity matrix. In addition to ensuring local optimality a global optimization step is used to optimize the solution across all bisections. Agglomerative Agglomerative clustering is a bottom-up strategy that initially treats each trajectory as an individual cluster and merges similar clusters hierarchically in a tree-like structure, stopping when only K clusters remain. Graph (min-cut) Similar to the divisive clustering method, graph methods seek to divide the full dataset into individual clusters. Instead of operating directly on the similarity matrix, a nearest neighbor graph is constructed where a trajectory is a vertex. Each vertex is connected by a weighted edge to its most similar trajectories. The K clusters are found using a min-cut partitioning algorithm which ﬁnds a division of the graph with minimal loss of edge weights.

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Clustering Validation c1 c2 c3 Ground truth clusters c2 c1 c3 Clusters to evaluated Hungarian Algorithms to maximize The number of clusters matched Accuracy=n_matched/n_total

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Evaluation Dataset CLUTO CLUTO is a software package for clustering low- and high-dimensional datasets and for analyzing the characteristics of the various clusters. Standalone program scluster is utilized for clustering trajectories 1032 trajectories 18 clusters Lankershim Dataset

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How the size of Gaussian Kernel function influences the converting from distance matrix to similarity matrix: σ should be large enough Evaluation-Distance Metrics DTW + Agglomerative σ accuracy

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How the size of Gaussian Kernel function influences the converting from distance matrix to similarity matrix: σ should be large enough Evaluation-Distance Metrics DTW + Divisive accuracy

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How the size of Gaussian Kernel function influences the converting from distance matrix to similarity matrix: σ should be large enough Evaluation-Distance Metrics Modified_Euclidean + Divisive

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Evaluation-Distance Metrics How (δ, ε)parameters of LCSS influences the clustering results δ LCSS+ Graph

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Evaluation-Clustering How (δ, ε)parameters of LCSS influences the clustering results ε LCSS+ Graph

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Evaluation-Clustering Modified_Euclidean, DTW σ=7.1 LCSS δ=3, ε=8 d1-Modified Euclidean, d2-DTW, d3-LCSS c1-divisive, c2-agglomerative, c3-graph Distance Metric d1 d2 d3 Clustering c1c2c3c1c2c3c1c2c3 Accuracy0.830.570.8220.9770.830.9170.9560.910.959 Distance Computation Time(s) 0.0015 0.15 0.02 Clustering Computation Time(s) 2.8590.3590.2972.7820.3750.3053.0310.3280.532

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Conclusion Distance Metric Computation Complexity d1

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Demo

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Thanks

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