Shoji Hirano Shusaku Tsumoto hirano@ieee tsumoto@computer Dept of Medical Informatics,

1. Clustering of Trajectory Data obtained from Soccer Game Record -A First Step to Behavioral Modeling                       Shoji Hirano Shusaku Tsumotohirano@ieee.orgtsumoto@computer.org Dept of Medical Informatics, Shimane Univ. School of Medicine, Japan

2. Outline • Introduction • Data Structure • Method • Experimental Results • Conclusions and Future Work

3. 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)

4. 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

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

6. Data Structure • Field geometry and Pass sequence 5346 Y IN GOAL PASS start X t -3500 3500 -5346

7. 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 DataLow interaction -> Sparse Data • Need for Multiscale Observation • Strategy -> global pass featureTactics -> local pass feature • Both exist concurrently It is required to partly change comparison scale according to the granularity of data and type of events Dense Sparse

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

9. segment MatchedPairs 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 Scale s Sequence A Sequence B

10. 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 s : • Scale s controls the degree of smoothing • s = small： local feature, s = large： global feature Scale s

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

12. IN GOAL B4(1) B6(0) B2(2) B3(1) B5(0) B1(2) B2(1) B4(0) Sequence B B2(0) B1(1) B3(0) B0(1) B0(2) B1(0) B0(0) Inflection Points IN GOAL A4(0) A2(1) A2(2) A3(0) A1(1) A1(2) A2(0) Sequence A t A0(2) A0(1) A1(0) A0(0) Scale 0 Scale 1 Scale 2 Matching Procedure

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

14. 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 Indiscernibility-based Clustering: Overview • 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.

15. 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

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

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

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

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

20. 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

21. 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.

22. 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

23. 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

24. Matching Criteria • 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 Overlap Gap a2 a1 a4 a3 A a5 b2 b4 P : Number of matched segment pairs b1 b3 b5 B ：dissimiarity of segments

25. 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. match Scale n Scale 2 no-match Scale 1

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