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Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 8 November 2012 Marian-Andrei Rizoiu ERIC Laboratory Julien Velcin Université Lumière Lyon 2 Stéphane Lallich France M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) φ 1 φ 2 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) φ 1 φ 2 t 1 t 2 t 3 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) t 1 φ 1 t 2 t 3 t 1 φ 2 t 2 t 3 t 1 t 2 t 3 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) d t 1 x 1 φ 1 t 2 t 3 d t 1 x 4 φ 2 t 2 t 3 t 1 t 2 t 3 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) d t 1 x 1 d φ 1 t 2 x 2 t 3 d t 1 x 4 d φ 2 t 2 x 5 t 3 t 1 t 2 t 3 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion the values for a certain number of numerical Dataset: features ( x d ) for multiple entities ( φ ) at different moments of time ( t ) d t 1 x 1 d φ 1 t 2 x 2 d t 3 x 3 d t 1 x 4 d φ 2 t 2 x 5 d t 3 x 6 t 1 t 2 t 3 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 2

Problem Proposed Solutions Experiments Conclusion Goal: Detect typical evolution patterns of individuals in the dataset M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 3

Problem Proposed Solutions Experiments Conclusion Goal: Detect typical evolution patterns of individuals in the dataset a) the phases through which the entity collection went over time M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 3

Problem Proposed Solutions Experiments Conclusion Goal: Detect typical evolution patterns of individuals in the dataset a) the phases through which the entity collection went over time b) the trajectory of entities through the different phases M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 3

Problem Proposed Solutions Experiments Conclusion Summary: 1. Problem 1.1 Data 1.2 Goal 2. Proposed solutions: 2.1 A clustering solution 2.2 Temporal-Aware Dissimilarity Measure 2.3 Contiguity Penalty Measure 2.4 TDCK-Means algorithm 2.5 Evaluation measures 3. Experiments 3.1 Qualitative evaluation 3.2 Quantitative evaluation 4. Conclusion and perspectives M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 4

Problem Proposed Solutions Experiments Conclusion Proposed solution: A temporal-aware constrained clustering algorithm, resulted clusters serve as phases. M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 5

Problem Proposed Solutions Experiments Conclusion Proposed solution: A temporal-aware constrained clustering algorithm, resulted clusters serve as phases. The resulted partition must ensure: - the descriptive coherence of clusters; - the temporal coherence of clusters; - continuous segmentation of observations belonging to an entity. M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 5

Problem Proposed Solutions Experiments Conclusion Proposed solution: A temporal-aware constrained clustering algorithm, resulted clusters serve as phases. The resulted partition must ensure: - the descriptive coherence of clusters; Temporal-aware - the temporal coherence of clusters; dissimilarity measure - continuous segmentation of Contiguity penalty observations belonging to an entity. measure M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 5

Problem Proposed Solutions Experiments Conclusion Proposed solution: A temporal-aware constrained clustering algorithm, resulted clusters serve as phases. The resulted partition must ensure: - the descriptive coherence of clusters; Temporal-aware - the temporal coherence of clusters; dissimilarity measure - continuous segmentation of Contiguity penalty observations belonging to an entity. measure K-Means like algorithm. Objective function to minimize: J = ∑ μ j ∈ M ∑ x i ∈ C j ( ∥ x i − μ j ∥ ∑ w ( x i , x k ) ) TE + φ = x i φ ) ( x k ∉ C j )∧( x k M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 5

Problem Proposed Solutions Experiments Conclusion Proposed solution: A temporal-aware constrained clustering algorithm, resulted clusters serve as phases. The resulted partition must ensure: 1 - the descriptive coherence of clusters; Temporal-aware - the temporal coherence of clusters; dissimilarity measure - continuous segmentation of Contiguity penalty observations belonging to an entity. measure 2 K-Means like algorithm. Objective function to minimize: J = ∑ μ j ∈ M ∑ x i ∈ C j ( ∥ x i − μ j ∥ ∑ w ( x i , x k ) ) TE + φ = x i φ ) ( x k ∉ C j )∧( x k 1 2 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 5

Problem Proposed Solutions Experiments Conclusion Euclidean distance distance in the description space M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 6

Problem Proposed Solutions Experiments Conclusion Euclidean distance distance in the description space Temporal-aware distance in both description dissimilarity measure space and temporal space M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 6

Problem Proposed Solutions Experiments Conclusion Euclidean distance distance in the description space Temporal-aware distance in both description dissimilarity measure space and temporal space ∥ x i − x j ∥ TE = 1 − ( 1 −∥ x i ∆ x max )( 1 −∣ x i ∆t max ) d − x j d ∥ 2 t − x j t ∣ 2 M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 6

Problem Proposed Solutions Experiments Conclusion Euclidean distance distance in the description space Temporal-aware distance in both description dissimilarity measure space and temporal space ∥ x i − x j ∥ TE = 1 − ( 1 −∥ x i ∆ x max )( 1 −∣ x i ∆t max ) d − x j d ∥ 2 t − x j t ∣ 2 Properties: ∥ x i − x j ∥ TE ∈[ 0,1 ] , ∀ x i , x j ∈ X d = x j d ∧ x i t = x j t ∥ x i − x j ∥ TE = 0 ⇔ x i d − x j d ∥= ∆ x max ∨∣ x i t − x j t ∣= ∆t max ∥ x i − x j ∥ TE = 1 ⇔∥ x i M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 6

Problem Proposed Solutions Experiments Conclusion Semi-Supervised pair-wise apply penalty when clustering constraints constraints are broken [Wagstaff & Cardie '00] M-A. Rizoiu, J. Velcin and S. Lallich Structuring Typical Evolutions using Temporal-Driven Constrained Clustering 7