Clustering of Trajectory Data obtained from Soccer Game Record -A First Step to Behavioral Modeling Shoji Hirano Shusaku Tsumoto Dept of Medical Informatics, Shimane Univ. School of Medicine, Japan

Outline Introduction Data Structure Method Experimental Results Conclusions and Future Work

Introduction Clustering of Spatio-temporal Data Provides a way to discover interesting characteristics about the motion of targets Related field: meteorology, medical image analysis, sports, crime research etc. Approaches Spatial clustering + temporal continuity trace (e.g. tracking of moving object) Spatial clustering based on temporal correlation (e.g. fMRI analysis) Spatial clustering + observation of the temporal changes of the clusters (e.g. Observation of the climate regimes)

Objective Development of a clustering method for trajectories with multiscale structural comparison scheme Compare trajectories according to both local and global views. Visualize common characteristics of trajectories Application: Clustering of trajectories of passes in soccer game records Discovery of interesting spatio-temporal patterns of passes which may reflect the strategy and tactics of the team Globally similar passes: strategy of the team -ex. Attack from right side Locally similar passes: tactics of the ream -x. Frequent use of one-two passes

Data Structure Soccer game records （ provided for research purpose by DataStadium Inc., Japan)

Data Structure Field geometry and Pass sequence X Y PASS start IN GOAL t

Pass sequence clustering: Problems Irregularly-sampled spatio-temporal sequence Data point is generated when a player takes an interaction with a ball High interaction -> Dense Data Low interaction -> Sparse Data Need for Multiscale Observation Strategy -> global pass feature Tactics -> local pass feature Both exist concurrently It is required to partly change comparison scale according to the granularity of data and type of events Sparse Dense

Trajectory Mining Preprocessing Segmentation and Generation of Multiscale Trajectories Segment Hierarchy Trace and Matching Calculation of Dissimilarities Clustering of Trajectories

Method: Multiscale Matching A pattern matching method that compares structural similarity of planar curves across multiple observation scales Able to compare objects by partly changing observation scales Simultaneously compare both global and local similarities Sequence A Sequence B Scale  Matched Pairs segment

Multiscale Description (Witkin et al 1984, Mokhatan et al. 1986) Describe convex/concave structure at multiple scales Sequence description ： t : course parameter Sequence x(t) at scale  Scale  controls the degree of smoothing  = small ： local feature,  large ： global feature Scale 

Multiscale Matching based on Convex/Concave Structure of Segments (Ueda et al. 1990) Segment: Partial sequence between adjacent inflection points Curvature K (t,  ) at scale  Inflection point: Represent a sequence as a set of segments Scale 

Matching Procedure Sequence A Sequence B Inflection Points Scale 0Scale 1Scale 2 IN GOAL A 0 (0) A 1 (0) A 2 (0) A 3 (0) A 4 (0) B 2 (0) B 0 (0) B 5 (0) B 6 (0) B 3 (0) B 4 (0) B 1 (0) B 0 (1) B 1 (1) B 2 (1) B 3 (1) B 4 (1) B 0 (2) B 1 (2) B 2 (2) A 0 (1) A 2 (1) A 1 (1) A 0 (2) A 2 (2) A 1 (2) t

Segment Dissimilarity Dissimilarity of Segments Dissimilarity of sequences Length Segment ai(k) Segment bi(j) Rotation Angle Max(, ) P: the number of matched pairs

Indiscernibility-based Clustering: Overview 1.Assignment of initial equivalence relations (ERs) Assign an initial ER to each of the N objects. An ER independently performs binary classification, similar or dissimilar, based on the relative proximity. Indiscernible objects under all of the N ERs form a cluster. 2.Iterative refinement of initial ERs For each pair of objects, count the ratio of ERs that have ability to discriminate them (indiscernibility degree) If the number is small, assume that these ERs give too fine classification and disable their discrimination ability Iterate step2 until the clusters become stable

Experiments Data Game records of FIFA WorldCup 2002 (64 games, including all heats and finals) Number of goals: 168 (own goals excluded) Procedure Select series containing ‘ IN GOAL ’ event, and generate a total of 168 trajectories of 2-D ball location. For every possible pair of the trajectories, calculate dissimilarity by using multiscale matching. Group the trajectories by using the obtained dissimilarities and indiscernibility-based clustering

Experimental Results Cluster Constitution ClusterCases ClusterCases Note: 55.2% (7839/14196) of triplet in the dissimilarity matrix did not satisfy the triangular inequality due to matching failure

Experimental Results (cont ’ d) Cluster 1 (87 cases) Turkey vs Japan Italy vs Korea IN GOAL Matching Result Corner Kick – Goal Europe: 45, South America: 24, Asia: 9

Experimental Results (cont ’ d) Cluster 2 (24 cases) Poland vs Portugal Germany vs Cameroon IN GOAL Matching Result Complex Pass – Side attack- Goal Europe: 13, South America: 7, Asia: 3

Experimental Results (cont ’ d) Cluster 4 (16 cases) Slovenia vs Paraguay IN GOAL China vs Turkey Matching Result Side Change – Centering/Dribble – Goal Europe: 10, South America: 4, Africa: 2

Experimental Results (cont ’ d) Cluster 3 (17 cases) Side Change – Centering/Dribble – Goal (Intermediate cases between Cluster 2 and 4) Europe: 10, South America: 2, Africa: 2 Asia 2

Summary of Experimental Results Goal success patterns can be classified into 4 major groups (with 8 minor patterns) Patterns: complexity of pass sequences With additional information Dribble/Centering/Side change: European Style However, the differences are not statistically significant. Key is “Side Change” Players (Defenders) should take care of the other side of the ball movement. The higher complexity of pass transactions, the higher rate of goal success gains by side change.

Conclusions Presented a new scheme of spatio-temporal data mining Grouped similar patterns using multiscale comparison and indiscernibility-based clustering techniques. Visualized similar patterns using matching results. Application to real World Cup data: Grouping and visualization of interesting pass patterns: ex. Complex pass -> side attack -> goal

Future Work Technical Issues Numerical Evaluation Validation and improvement of segment dissimilarity measure; inclusion of event type to dissimilarity Apply the proposed method to all path series including non- ‘ IN GOAL ’ series Differences between success and failure are very small. This suggests that the patterns of soccer attack are simple. Apply the proposed method to medical environment Trajectories of Laboratory Examinations (IEEE ICDM06) Trajectories of Patients’ Movement: Patient Safety

Criteria for determining the best set of segment pairs Complete match; original sequence should be correctly formed by concatenating the selected segments without any overlaps or gaps Minimization of total segment difference Matching Criteria Overlap Gap P : Number of matched segment pairs A B a1 a2 a3 a4 a5 b1 b2 b3 b4 b5 ： dissimiarity of segments

Matching Failure Problem in MSM Theoretically, any sequence can finally become a single segment at enough high scales. Therefore, any pair of sequences should be successfully matched. Practically, there should be an upper limit of scales in order to reduce computational complexity. Therefore, the number of segments can be different even at the highest scales. If matching is not successful, the method should return infinite dissimilarity or a magic value that indicates matching failure. Scale 1 Scale 2 Scale n no-match match

Trajectory Mining Preprocessing Segmentation and Generation of Multiscale Trajectories Segment Hierarchy Trace and Matching Calculation of Dissimilarities Clustering of Trajectories