Fair Use Agreement

1. Fair Use Agreement • This agreement covers the use of all slides on this CD-Rom, please read carefully. • You may freely use these slides for teaching, if • You send me an email telling me the class number/ university in advance. • My name and email address appears on the first slide (if you are using all or most of the slides), or on each slide (if you are just taking a few slides). • You may freely use these slides for a conference presentation, if • You send me an email telling me the conference name in advance. • My name appears on each slide you use. • You may not use these slides for tutorials, or in a published work (tech report/ conference paper/ thesis/ journal etc). If you wish to do this, email me first, it is highly likely I will grant you permission. • (c) Eamonn Keogh, eamonn@cs.ucr.edu Themis Palpanas

2. Indexing Large Human-Motion Databases Eamonn Keogh, Themis Palpanas Victor B. Zordan,Dimitrios Gunopulos University of California, Riverside Marc Cardle University of Cambridge

3. Motion Capture • records motion data from live actors Themis Palpanas

4. Motion Capture • records motion data from live actors • used for data-driven animation Themis Palpanas

5. Motion Capture in Games Industry Street NBA Madden Themis Palpanas

6. Motion Capture in Movie Industry Troy Lord of the Rings Themis Palpanas

7. Motivation • motion capture data • segmented in short sequences, stored in motion libraries • composed to create long, realistic motion sequences • important to find similar sequences • form pool of similar sequences • choose the most promising, to continue the motion Themis Palpanas

8. Motivation • Dynamic Time Warping (DTW) • Considers only local adjustments in time, to match two time series • However sometimes global adjustments are required • DTW is being extensively used • uniform scaling is complementary • combination of both techniques offers rich, high-quality result set Uniform Scaling DTW Themis Palpanas

9. C Q 0 0 100 100 200 200 300 300 400 400 Uniform Scaling • time series • query, Q, length n • candidate, C, length m (m>n) Themis Palpanas

10. C Q 0 0 100 100 200 200 300 300 400 400 Q 0 0 100 100 200 200 300 300 400 400 Uniform Scaling • time series • query, Q, length n • candidate, C, length m (m>n) • stretch Q to length p (n≤p≤m): Qp • Qpj = Q┌j*n/p┐, 1 ≤ j ≤ p • scaling factor, sf = p/n • max scaling factor, sfmax= m/n Qp Themis Palpanas

11. Problem Statement • given • time series, Q • database of candidate time series, {D} • find argminp{ dist(Qp, {D} ) } • dist(Qp, {D} )= Euclidean Distance between time series Themis Palpanas

12. Problem Statement • given • time series, Q • database of candidate time series, {D} • find argminp{ dist(Qp, {D} ) } • dist(Qp, {D} )= Euclidean Distance between time series • challenges • quickly solve the problem for two time series • extend solution to scale-up to large time series databases Themis Palpanas

13. Outline • Speeding Up Search • Scaling Up To Large Databases • Experimental Evaluation • Related Work • Conclusions Themis Palpanas

14. Best Uniform Scaling Match • brute force algorithm: • for each time series in {D} for each sf, 1 ≤ sf ≤ sfmax compute distance between the two time series find the best overall match • time complexity: O(|D|(m-n)) • extremely expensive! Themis Palpanas

15. Lower Bounding Uniform Scaling • lower bound distance between two time series, for any sf, 1 ≤ sf ≤ sfmax • desiderata: • fast to compute • tight bound • results in fast pruning of candidates that are guaranteed not to belong to the solution • compute distance only for time series not pruned by lower bound Themis Palpanas

16. Lower Bounding Uniform Scaling • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 C m = 100 0 10 20 30 40 50 60 70 80 100 90 Themis Palpanas

17. Lower Bounding Uniform Scaling • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 • build envelopes, length 80: U n = 80 Ui = max( C (i-1)*m/n +1,…, C i*m/n) Li = min( C (i-1)*m/n +1,…, C i*m/n) L 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

18. Lower Bounding Uniform Scaling Q • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 • build envelopes, length 80: Ui = max( C (i-1)*m/n +1,…, C i*m/n) Li = min( C (i-1)*m/n +1,…, C i*m/n) 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

19. Lower Bounding Uniform Scaling • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 • build envelopes, length 80: Ui = max( C (i-1)*m/n +1,…, C i*m/n) Li = min( C (i-1)*m/n +1,…, C i*m/n) 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

20. Lower Bounding Uniform Scaling • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 • compute lower bound: 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

21. Envelope Indexing • dimensionality of envelopes is high 80 points 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

22. Envelope Indexing • dimensionality of envelopes is high • reduce dimensionality by approximating them • Piecewise Constant Approximation 8 points 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

23. Envelope Indexing • dimensionality of envelopes is high • reduce dimensionality by approximating them • Piecewise Constant Approximation • assume query Q, length 80 Q 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

24. Envelope Indexing • dimensionality of envelopes is high • reduce dimensionality by approximating them • Piecewise Constant Approximation • assume query Q, length 80 • we approximate it with 8 points 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

25. Envelope Indexing • dimensionality of envelopes is high • reduce dimensionality by approximating them • Piecewise Constant Approximation • assume query Q, length 80 • approximated with 8 points • compute approximation of lower bound: 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas

26. Algorithms for Secondary Storage • use a multidimensional index • VA-file -> FastScan algorithm • R-tree -> RtreeProbe algorithm • 2-pass algorithms: 1. scan approximated envelopes, prune search space 2. find exact answer using original series Themis Palpanas

27. Outline • Speeding Up Search • Scaling Up To Large Databases • Experimental Evaluation • Related Work • Conclusions Themis Palpanas

28. Datasets Used • motion capture • data from 124 sensors placed on human actors • mixed bag • time series coming from: • medicine, manufacturing, environmental monitoring, economics, sensor data • experimented with time series databases of: • size 5,000 – 80,000 • time series length 64 – 1,024 points Themis Palpanas

29. 0.25 CD- criterion 0.2 0.15 LB_Keogh 0.1 0.05 0 1.20 256 1.10 128 64 1.05 256 128 64 Main Memory Experiments • assume database fits in memory • measure pruning power: • fraction of times each approach calls distance function • our technique: • 1 order of magnitude faster than CD-criterion Themis Palpanas

30. 0.25 CD- criterion 0.2 0.15 LB_Keogh 0.1 0.05 0 1.20 256 1.10 128 64 1.05 256 128 64 Main Memory Experiments brute force • assume database fits in memory • measure pruning power: • fraction of times each approach calls distance function • our technique: • 1 order of magnitude faster than CD-criterion • 3 orders of magnitude faster than brute force Themis Palpanas

31. 25 25 20 20 15 15 Seconds Seconds 10 10 5 5 0 0 256 256 128 128 64 64 LinearScan LinearScan 256 256 128 128 64 64 FastScan FastScan 1.20 1.20 256 256 1.10 1.10 128 128 1.05 1.05 64 64 RtreeProbe RtreeProbe Disk-Based Experiments • comparison of: • brute force • FastScan • RtreeProbe Themis Palpanas

32. Disk-Based Experiments • comparison of: • FastScan • RtreeProbe Themis Palpanas

33. Disk-Based Experiments • comparison of: • FastScan • RtreeProbe Themis Palpanas

34. Case Study • video Themis Palpanas

35. Outline • Speeding Up Search • Scaling Up To Large Databases • Experimental Evaluation • Related Work • Conclusions Themis Palpanas

36. Related Work • Dynamic Time Warping (DTW) • [Yi & Faloutsos’00][Keogh’02][Zhu & Shasha’03][Fung & Wong’03] • Longest Common SubSequence (LCSS) • [Das et al.’97][Vlachos et al.’03] • uniform scaling • [Argyros & Ermopoulos’03] Themis Palpanas

37. Outline • Speeding Up Search • Scaling Up To Large Databases • Experimental Evaluation • Related Work • Conclusions Themis Palpanas

38. Conclusions • studied utility of uniform scaling similarity matching • applications in: • motion capture libraries, music retrieval, historical handwritten archives • introduced first lower bounding technique • proposed indexing method for bounding envelopes • suitable for very large time series databases • experimentally evaluated efficiency of technique • demonstrated quality of results with real motion capture data Themis Palpanas

39. Outline Themis Palpanas

40. Lower Bounding Uniform Scaling • assume: • candidate C, length 100 • query Q, length 80 • wish to find best match for any scaling of Q between 80-100 • build envelopes, length 80: Ui = max( C (i-1)*m/n +1,…, C i*m/n) Li = min( C (i-1)*m/n +1,…, C i*m/n) 0 10 20 30 40 50 60 70 80 90 100 Themis Palpanas