Recommended
More Related Content
Recently uploaded
Recently uploaded (20)
Featured
Featured (20)
Similar search with trillions of time series
- 1. Searching and Mining Trillions of Time Series Subsequences under Dynamic Time Warping Thanawin Rakthanmanon, Bilson Campana, Abdullah Mueen, Gustavo Batista, Brandon Westover, Qiang Zhu, Jesin Zakaria, Eamonn Keogh Hoan Nguyen – Trung Minh Nguyen
- 2. 2 Abstract Optimizations to search and mine large databases very fast
- 4. 4 Problem Similarity search is an important part of most time series data mining algorithm. Dynamic Time Warping is the best measure to use but slow.
- 5. 5 Definitions Time series Time series T is an ordered list: T = t1, t2, … ,tm
- 6. 6 Definitions Subsequence Subsequence Ti,k of time series T is a time series of length k start at position i: T = t1, t2, … ,tm
- 8. 8 Related work Known optimizations Squared distance
- 9. 9 Related work Known optimizations Lower bounding LB_KimFL LB_Keogh
- 10. 10 Related work Known optimizations Early abandon
- 11. 11 Method Early abandon Z-Normalization Q T T3 T2 T1 Z-Normalization Q’ T3’ T2’ T1’ … Long Time series Subsequences Normalized Subsequences Query Normalized Query Normal approach
- 12. 12 Method Early abandon Z-Normalization Novel approach Early abandon with Z-normalization 1. Query is Z-normalized 2. Z-normalization of each subsequence will be calculated on the fly with the distance calculation. 3. If distance > best_so_far then early abandon both calculation
- 13. 13 Method Re-ordering Early Abandoning Ordering is created based on the query.
- 14. 14 Method Cascading Lower Bounds Lower bounds are used in a cascade to prune candidates.
- 15. 15 Results Comparison between: Naïve - Z-normalization from start - full ED(DTW) calculation State-of-the-art (SOTA) - Z-normalization from start - early abandoning - LB_Keogh bounding for DTW UCRSuite
- 16. 16 Results Baseline Tests on Random Walk 0 5000 10000 15000 20000 25000 30000 Million Billion Trillion minutes UCR-ED SOTA-ED UCR-DTW SOTA-DTW
- 17. 17 Results Baseline Tests on Random Walk 0 500 1000 1500 2000 2500 Million Billion seconds UCR-ED SOTA-ED UCR-DTW SOTA-DTW
- 18. 18 Results Baseline Tests on Random Walk
- 20. 20 Conclusion - The approach is very simple yet so effective. - These optimizations can be applied to most measures but may not work for some, like: Hamming distance