In Search of Meaning for Time Series Subsequence Clustering

1. In Search of Meaning for TimeSeries Subsequence Clustering Dina Goldin, Brown University work done with Ricardo Mardales, UConnand George Nagy, RPI CIKM, Nov. 8, 2006

2. The “Meaningless” Paper [KLT03]Keogh, E., Lin, J., Truppel, W. Clustering of Time Series is meaningless. Proc. IEEE Conf. on Data Mining (2003) [KL05] Keogh, E. & Lin, J. Clustering of time-series subsequences is meaning-less: implications for previous and future research. J. Knowledge and Inf. Sys. 8:2 (2005) Clustering of time series subsequences is meaningless [because] the result of clustering these subsequences is independent of the input. CIKM’06

3. Implications of “Meaningless” Result • It “cast a shadow over STS clustering”. • Jeopardized the legitimacy of research that had used subsequence clustering. • Led to a flurry of follow-up research • Chen ’05 uses cyclical data and k-medoids • Simon et al. ’05 uses self-organizing maps • Denton ’04 uses density based clustering • Struzik ’03 uses correlation for trivial matches • Bagnall ’03, Mahoney ’05, Rodrigues et al. ’04 moved away from STS • No one had challenged the results head-on • i.e. show that output and input of STS clustering are not independent CIKM’06

4. Independence of Input and Output Time series: x y STS clusteringalgorithm Clusters: A C B Is there a way to match C to the right time series (X or Y) reliably? • Before: NO;cluster_set_dist(C,B) / cluster_set_dist(C,A) not small Our work: YES Find a different distance measure! CIKM’06

5. Outline • Introduction • New Distance Measure for Cluster Setsbased on the notion of cluster shapes • STS Cluster Matching • Observations and Conclusions CIKM’06

6. STS Clustering • Consider all subsequences of the same time series • time series T of length m, window Size w • Normalize each subsequence so its average is 0 and std. deviation is 1 • Normalize(x) = x – avg(x) / stddev(x) • Cluster the normalized subsequences using K-means clustering algorithm CIKM’06

7. Cluster Centers K-means Clustering • Given a set of multidimensional points (of dimension w), partition in into K groups, so each point belongs to one cluster. • Compute the center of each cluster; it is the mean of all points in the cluster. • Result: a set of Kcluster centers CIKM’06

8. Cluster Set Distance - Previous approach to measuring distance between cluster sets - Returs sum of Euclidean Distances between cluster centers A B cluster_set_dist(B,A) CIKM’06

9. Z X Shape of cluster A = [XZ, ZY, XY] A B Y Cluster Shape Distance • New distance measure for cluster sets • Returns Euclidean Distance between cluster set shapes • Cluster set shape: sorted list of pairwise distances between cluster centers; has K*(K-1)/2 values A and B have the same shape(B is a rotated and translated copy of A) so cluster_shape_dist(A,B) = 0 CIKM’06

10. Cluster Shape Example • STS clustering for ocean series with K=3 • Note: all our datasets come from UC Riverside repository D’s: pairwise distancesbetween cluster centers CIKM’06

11. Cluster Structure • Sort the pairwise distances • Observation: for each K and w, the shapes obtained from different STS clustering runs are similar! • Cluster structure DT: the average of cluster set shapes from many clustering runs over T. CIKM’06

12. k=4 w=8 Cluster Structure: Example • Cluster structures for datasets from UCR repository k=3 w=8 k=3 w=16 CIKM’06

13. Outline • Introduction • New Distance Measure for Cluster Sets • STS Cluster Matching • Observations and Conclusions CIKM’06

14. STS Cluster Matching Problem Given a dataset of multiple time series and a cluster center set from one of them (“query”), match it to the series that produced it. Note: K and w are assumed to be fixed. • Matching algorithm: Outputs a guess -- which of the N time series in the dataset produced the query? • Algorithm accuracy: Percentage of times that the matching algorithm is correct. Note: no previous work succeeded to attain high accuracy, even with dataset of size 2! CIKM’06

15. Matching Algorithm • Pre-processing phase: • For each sequence in the dataset, perform Q clustering runs with given K and w, and calculate its cluster structure. • Store all the structures in a master table. • Matching phase: 1. Given a query, find the Euclidean distance from its shape to each of the structures in the master table. 2. Return the sequence whose structure is the closest. CIKM’06

16. Master table k=3 w=8 Example CIKM’06

17. Performance Evaluation • 10 datasets from UCR time series repository • 100 clustering runs per structure • Algorithm evaluated with 3 values of K, 4 values of w (12 combinations) Result: 100% accuracy CIKM’06

18. Outline • Introduction • New Distance Measure for Cluster Sets • STS Cluster Matching Algorithm • Observations and Conclusions CIKM’06

19. Conclusions • Previous work seemed to show that the output of STS clustering is independent of input. • The correct conclusion: cluster set distance is an inappropriate distance metric. • Instead of absolute positions of cluster centers, one needs to use relative positions (as represented by cluster shapes). • STS clustering becomes meaningful: cluster centers are reliably matched to original series. • We also found correlation between some characteristics (number of unique shapes, shape skew) and sequence smoothness. CIKM’06

20. Future Work WHY? • Difference in behavior between whole-sequence and subsequence clustering?(some preliminary answers are in paper) • Apparent presence of transformations among cluster sets? • Dependency between smoothness, skew, number of unique clusters, etc.? HOW? • Find expected accuracy of the matching algorithm for given input and Q (number of clustering runs to compute each structure). CIKM’06

21. Questions?

22. Thank you!