Time Series Sequence Matching

1. Time Series Sequence Matching Jiaqin Wang CMPS 565

2. Papers • “Fast subsequence Matching in time-series database”Christos Faloutsos, M.Ranganathan Yannis Manolopoulos • “Skyline index for time series data”Quanzhong Li, Ines Fernando Vega Lopez, Bongki Moon

3. Types of Time Series sequence • Financial, marketing area • Stock prices • Sales numbers • Scientific databases • Weather data • Environmental data

4. Categories for time series sequencematching • Whole matching • data sequences and query sequence have the same length • Subsequence matching • Query sequence and data sequence have different length

5. Whole matching • Given N sequences with the same length l • Use features extraction function to convert sequences into n-dimensional values • DFT • N-dimensional value (Q1,Q2,…,Qn) • Most energy in first few coefficients • Keep first few coefficients • Reduce dimensions of sequence

6. Whole matching • Map each sequence as a n-dimensional point into the feature space • Only take first 2 coefficients • Organize these points into R-tree • For index and search in R-tree

7. Whole matching • New coming query sequence • Use DFT convert to feature point • Map the query feature point into feature space • Find out points whose distance to query point within tolerance e • Consider them similar

8. Some pictures of time series data and DFT • Discrete Fourier Transform (DFT ) • keep first few (2-3) coefficients • The first few coefficients contain most energy of the feature

9. Feature space • TS1(0.05,3) • TS2(0.01,12) • ……

10. Feature space • The distance e < minimum query distance

11. Subsequence matching • A collection of N sequences, each one has different length • A query Q with tolerance e • Find out all sequence Sі(1<i<N), along with the correct offsets k,such that the sequence Sі[k:k+Len(Q)-1] matches the query sequence: D(Q, Sі[k:k+Len(Q)-1] ) <= e

12. ST-index • Assuming the minimum query length w • Using a sliding window of size w and place it on the date sequence at every possible offsets of the whole data sequences • Extract the features in window at each possible offset and map each feature as a point into feature space

13. Figure • Sliding window on sequence from offset 0 to Len(S)-w+1 • The length of window is w

14. Figure • Sliding window on sequence from offset 0 to Len(S)-w+1 • The length of window is w

15. Figure • Sliding window on sequence from offset 0 to Len(S)-w+1 • The length of window is w

16. Figure • Sliding window on sequence from offset 0 to Len(S)-w+1 • The length of window is w

17. Figure • Sliding window on sequence from offset 0 to Len(S)-w+1 • The length of window is w

18. Result • A series of points in the feature space is curve • R-tree

19. MBRs • Store points in R-tree is inefficient • Divide trial into sub-trials using minimum bounding rectangles (MBRs)

20. MBRs in R-tree • Combine small MBRs • Get the index information

21. How to insert points into MBRs • Group the points into MBR with a fixed-number • Group the points into MBR with a variable-number

22. I-adaptive method • One greedy algorithm • number of disk access • cost function • average cost function

23. Algorithm • Assign the first point of the trail in a sub-trail • For each successive point • If it increases the average cost of current sub-trail • Then start another sub-trail • Else include this point in current sub-trial

24. Skyline index for time series data • “Skyline index for time series data”Quanzhong Li, Ines Fernando Vega Lopez, Bongki Moon

25. Adaptive Piecewise Constant Approximation (APCA) • What is APCA?

26. Adaptive Piecewise Constant Approximation (APCA) • Limitation of APCA • Internal overlap in MBRs

27. Skyline Bounding Region (SBR) • SBR • N time series data objects of length l • Specify 2-dimensional regions by top and bottom skylines

28. Approximate SBR • Many approaches • Equal-length constant-valued segments • Variance-length constant-valued segments • ASBR will cover the original SBR

29. Index Approximation SBR • R-Tree based Skyline index • Internal node • Approximation SBR • Pointer to child node • Leaf node • Pointer to time series data

30. The End Thank You