1. Fast Time Series Classification Using Numerosity Reduction DME Paper Presentation Jonathan Millin & Jonathan Sedar Fri 12 th Feb 2010

2. Fast Time Series Classification Using Numerosity Reduction Appearing in Proceedings of 23 rd International Conference on Machine Learning 2006. Authors: – Xiaopeng Xi, Eamonn Keogh, Christian Shelton, Li Wei, Computer Science & Engineering Dept, UC Riverside, CA – Chorirat ‘Ann’ Ratanamahatana. Dept of Computer Engineering, Chulalongkorn Uni, Bangkok Cited by 34 papers (Google Scholar)

3. Overview High classification accuracy on time-series data is achieved using Dynamic Time Warping and a novel application of numerosity reduction to efficiently reduce computational complexity. Fast Time Series Classification Using Numerosity Reduction

4. Agenda Introduction Methods – Dynamic Time Warping – Numerosity Reduction – Adaptive Warping Window (AWARD) – Fast AWARD Results Discussion Fast Time Series Classification Using Numerosity Reduction

5. Time-Series Data Classification Classifying through pattern matching Time Series ClassificationIntroduction

6. What is Dynamic Time Warping? Compare similar time series allowing for temporal skew: Dynamic Time WarpingMethods

7. How does DTW Work? Dynamic Time Warping Align series Construct distance matrix Find optimal warping path Introduce warping window to reduce complexity Methods

8. DTW Performance Dynamic Time Warping Reported comparisons Fig. 3 Figs. 4,5,7 Test sets (shown later) Methods

9. DTW Vs Literature ECG Xi et al. (2006) use 1NN-DTW and Euclidian Distance: ‘perfect accuracy’ Kim & Smyth et al. (2004) use HMM: 98% accuracy Lighting (FORTE-2) Xi et al. (2006) use 1NN-DTW: error rate 9.09% Eads & Glocer et al. (2005) use grammar guided feature extraction: error rate 13.22% Dynamic Time Warping ControlChart Xi et al. (2006) use 1NN-DTW: error rate 0.33% Rodriguez & Alonso et al (2000) use 1 st order logic rules with boosting: error rate 3.6% Nanopolus & Alcock et al. (2001) use multi-layer perceptron NN: error rate 1.9% Wu & Chang (2004) use ‘super kernel fusion’: error rate 0.79% Chen & Kamel (2005) use ‘Static Minimization-Maximization approach’: best error rate 7.2% Methods

10. Dynamic Time Warping DTW is ‘at least as accurate’ as Euclidean distance Methods

11. DTW gives great results, but Naive implementation is computationally expensive LB_Keogh reduces amortised cost to O(n) At the limits of DTW algorithm optimisation Look elsewhere for classification speed gains......Numerosity reduction Dynamic Time WarpingMethods

12. Numerosity Reduction Techniques Naive Rank Reduction Adaptive Warping Window (AWARD) Fast Numerosity Reduction (FastAWARD) Numerosity Reduction TechniquesMethods

13. Naive Rank Reduction Numerosity Reduction: Naive Rank Reduction x1x1 x2x2 d1d1 d2d2 d3d3 x3x3 x4x4 d 3 > d 4 > d 2 > d 1 x5x5 d4d4 Principle: remove instances in an order which minimises misclassifications. 1.Ranking (iterative O(n)) – Remove duplicates – Apply 1NN classification – Rank each x according to class of 1 st NN – Break ties by proximity of nearest class 2.Thresholding – User defined, (keep n highest, best n%) Methods

14. Classification accuracy declines when the size of the dataset decreases Naive Rank Reduction Numerosity Reduction: Naive Rank Reduction Larger r gives better accuracy on smaller datasets Motivates adaptive window Methods

15. Adaptive Warping Window (AWARD) What – Dynamically adjusting the window size during numerosity reduction Why – Larger windows give better accuracy on smaller datasets How – Initialise r to best warping size (exhaustive search r=1:100 ) – Begin Naïve Rank Reduction (shown earlier) – Tests accuracy of the reduced set with r and r+1 – If accuracy(r+1) > accuracy(r) then r++ Problems – Provides a better accuracy during numerosity reduction, but the additional checks increase complexity from O(n) to O(n 3 ) Numerosity Reduction: AWARDMethods

16. FastAWARD What – Essentially AWARD, but uses the calculations from previous iterations to reduce complexity Why – Reduce complexity to reduce execution time How – performs incremental updates after each step to reduce complexity of future steps Numerosity Reduction: FastAWARDMethods

17. How - Storing information Done by storing (for each i=r:100 ): – Nearest neighbour matrix ( A ) – Distance matrix ( B ) – Accuracy array ( ACC ) MethodsNumerosity Reduction: FastAWARD Q C r r ACC

18. How – Incremental Updates After each item is discarded: – Update A (Neighbors) – Update B (Distances) – Update ACC (Accuracy) – Check if ACC[r+1]>ACC[r] MethodsNumerosity Reduction: FastAWARD x1x1 x2x2 d1d1 d2d2 d3d3 bob x3x3 d 3 > d 4 > d 1 > d 2 x4x4 d4d4 x1x1 x2x2 d1d1 d new d4d4 x3x3 d new > d 1 > d 3 x4x4

19. Interim Recap Dynamic Time Warping accounts for skew Using AWARD numerosity reduction FastAWARD vs AWARD...Does it work? RecapMethods

20. Experiments (Accuracy) Experimental WorkResults

21. Experiments Experimental WorkResults

22. Experiments (Accuracy) etc Experimental WorkResults

23. Experiments (Efficiency) Massive improvements in efficiency of numerosity reduction process Experimental WorkResults

24. Experiments (Anytime Classification) Etc Experimental WorkResults

25. Summary 1NN-DTW is an excellent time series classifier DTW is computationally expensive because of the number of pattern matches DTW algorithm is at limits of optimisation Improve speeds by reducing number of required matches (Fast)AWARD adjusts the warping window with numerosity – increases accuracy FastAWARD is several orders of magnitude faster than AWARD SummaryDiscussion

26. Our Critique Two Patterns dataset seems cherry-picked DTW model may necessitate bespoke pre-processing RandomFix vs RankFix – very similar results AWARD efficiency comparisons ignore initialisation effort and speed wasn’t compared to other methods (RT1, 2, 3) Comparisons of r incomplete Anytime classification experiments seem rigged in favour of AWARD DiscussionOur Critique

27. Two Patterns dataset seems cherry- picked Reported comparisons Fig. 3 Figs. 4,5,7 Test sets (shown later) DiscussionOur Critique

28. DTW model may necessitate bespoke pre-processing DiscussionOur Critique

29. RandomFix vs RankFix - similar results DiscussionOur Critique

30. AWARD efficiency comparisons ignore initialisation effort and speed wasn’t compared to other methods (RT1, 2, 3) DiscussionOur Critique

31. Comparisons of r incomplete DiscussionOur Critique

32. Anytime classification is rigged? DiscussionOur Critique

33. Q&A Thank You.