1. 1 Novel Online Methods for Time Series Segmentation Xiaoyan Liu, Member, IEEE Computer Society, Zhenjiang Lin, andHuaiqing Wang IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 20, NO. 12, DECEMBER 2008 Adviser ︰ Yu-Chiang Li Speaker ︰ Yu-Hui Wu Date ︰ 2009/12/03

2. 2 Outline  Introduction  Related Work  Novel Online Segmentation Algorithms ︰ FSW and SFSW  Complexity Analysis  Experiments  Conclusions

3. 3 Introduction  Time series have increasing importance Finance Medicine Manufacturing  Approximate representation of the time series is one of the solutions Discrete Fourier Transform Discrete Wavelet Transform Singular Value Decomposition Piecewise Aggregate Approximation Piecewise Linear Approximation (PLA)

4. 4 Introduction  Piecewise Linear Approximation (PLA) Widely used Simplicity  Segmentation problem Representation quality Computing efficiency

5. 5 Related Work  Segmentation problem can be stated in the following form:

6. 6 Related Work  Segmentation methods Online Offline  complete sequences  Top-down algorithms unsegmented sequence introduce one cutting point

7. 7 Related Work  Bottom-up algorithms n-1 segments Each point is a segmenting point  SW(sliding windows) algorithms Online method and low computation complexity Lacking a global view

8. 8 Novel Online Segmentation Algorithms  Reduces the time complexity Maximum vertical distance (MVD)  FSW(Feasible space window)  SFSW(Stepwise feasible space window)

9. 9 Novel Online Segmentation Algorithm  Maximum Vertical Distance and Segmentation Criterion

10. 10 Novel Online Segmentation Algorithm  SW method can be reduced by using this segmentation criterion

11. 11 Novel Online Segmentation Algorithm  FSW method Candidate Segmenting Point (CSP)  Serch for the farthest CSP

12. 12 Novel Online Segmentation Algorithm

13. 13 Novel Online Segmentation Algorithm  SFSW method SW method lacking an overall view

14. 14 Novel Online Segmentation Algorithm  Intuitions behind the stepwise strategy

15. 15 Novel Online Segmentation Algorithm  Stepwise segmenting process

16. 16 Complexity Analysis  The worst case of FSW

17. 17 Complexity Analysis  SWAB Bottom-Up and SW SWAB is a small constant factor  SW Time to compute a single segment Time complexity or

18. 18 Complexity Analysis  FSW Finding one segmenting point is K segments in time series T  SFSW Time complexity of produce segment Time complexity of SFSW

19. 19 Complexity Analysis

20. 20 Experiments

21. 21 Experiments

22. 22 Experiments

23. 23 Conclusions  Successfully reduces the computational complexity of the classic SW method from to  FSW and SFSW methods always generate far fewer segments than the other two methods