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A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
A Unified Approach to Mining Complex Time-Series Data for ...
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  • 1. Outline Introduction Mining by Learning Conclusion A Unified Approach to Mining Complex Time-Series Data for Various Kinds of Patterns Yi Wang1 J.H. Feng1 J.Y. Wang1 Z.Q. Liu2 1 Department of Computer Science, Tsinghua University, Beijing, 100084, China 2 School of Creative Media, City University of Hong Kong, Hong Kong IEEE ICDM Conference, 2007 Wang, et al Mining Complex Time-Series Data
  • 2. Outline Introduction Mining by Learning Conclusion 1 Introduction Aspects of Sequential Data Mining Various Approaches or A Unified One 2 Mining by Learning Learning the Temporal Structure as A Graph Various Kinds of Hidden Markovian Models Learning VLHMM 3 Conclusion Mining Various Kinds of Patterns Contributions Wang, et al Mining Complex Time-Series Data
  • 3. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, Various Mining Goals: Difficulties: Wang, et al Mining Complex Time-Series Data
  • 4. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: Difficulties: Wang, et al Mining Complex Time-Series Data
  • 5. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: periodic pattern, Difficulties: two periodic patterns: one with 3 realizations, the other with 2. Wang, et al Mining Complex Time-Series Data
  • 6. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: periodic pattern, search-by-example, Difficulties: Wang, et al Mining Complex Time-Series Data
  • 7. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: periodic pattern, search-by-example, frequent atomic pattern, Difficulties: Wang, et al Mining Complex Time-Series Data
  • 8. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: periodic pattern, search-by-example, frequent atomic pattern, Difficulties: uncertainty on the y-axis (e.g., noise), match? Wang, et al Mining Complex Time-Series Data
  • 9. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Aspects of Sequential Data Mining Various Sequence Types: univariate/multivariate, integer (discrete)/ real (continous), Various Mining Goals: periodic pattern, search-by-example, frequent atomic pattern, Difficulties: uncertainty on the y-axis matches with which? or (e.g., noise), matches with both? uncertainty on the x-axis (e.g., time scale). Wang, et al Mining Complex Time-Series Data
  • 10. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Various Approaches or A Unified One Previous Research: Various approaches Our Work: Various types of Various mining Various mining sequences and algorithms resultsd difficulties The Unified Approach: Wang, et al Mining Complex Time-Series Data
  • 11. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Various Approaches or A Unified One Previous Research: Various approaches Our Work: Various types of Various mining Various mining sequences and algorithms resultsd A unified approach difficulties The Unified Approach: Wang, et al Mining Complex Time-Series Data
  • 12. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Various Approaches or A Unified One Previous Research: Various approaches Our Work: Various types of Various mining Various mining sequences and algorithms resultsd A unified approach difficulties The Unified Approach: Learning Temporal Graph Learns various types of hidden structure algorithms sequences by hidden Markovian as directed for Markovian models; model graph mining Wang, et al Mining Complex Time-Series Data
  • 13. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Various Approaches or A Unified One Previous Research: Various approaches Our Work: Various types of Various mining Various mining sequences and algorithms resultsd A unified approach difficulties The Unified Approach: Learning Temporal Graph Learns various types of hidden structure algorithms sequences by hidden Markovian as directed for Markovian models; model graph mining represents the temproal structure by a graph; and Wang, et al Mining Complex Time-Series Data
  • 14. Outline Introduction Mining by Learning Conclusion Aspects of the Problem A Unified Approach Various Approaches or A Unified One Previous Research: Various approaches Our Work: Various types of Various mining Various mining sequences and algorithms resultsd A unified approach difficulties The Unified Approach: Learning Temporal Graph Learns various types of hidden structure algorithms sequences by hidden Markovian as directed for Markovian models; model graph mining represents the temproal structure by a graph; and mines various patterns by well-studies graph algorithms. Wang, et al Mining Complex Time-Series Data
  • 15. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 16. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 17. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 18. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 19. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 20. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 21. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 22. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning the Temporal Structure as A Graph Wang, et al Mining Complex Time-Series Data
  • 23. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Hidden Markov Model (HMM) Given number of states, S, the number of contexts is S. Short contexts → inaccurate modeling. Wang, et al Mining Complex Time-Series Data
  • 24. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Hidden Markov Model (HMM) Given number of states, S, the number of contexts is S. Short contexts → inaccurate modeling. Wang, et al Mining Complex Time-Series Data
  • 25. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Hidden Markov Model (HMM) Given number of states, S, the number of contexts is S. Short contexts → inaccurate modeling. Wang, et al Mining Complex Time-Series Data
  • 26. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Hidden Markov Model (HMM) Given number of states, S, the number of contexts is S. Short contexts → inaccurate modeling. Wang, et al Mining Complex Time-Series Data
  • 27. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Fixed nth-order Hidden Markov Model (n-HMM) Given number of states, S, and the length of context, n, the number of contexts is S n . Long contexts → accurate modeling, but inefficient learning. Wang, et al Mining Complex Time-Series Data
  • 28. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Fixed nth-order Hidden Markov Model (n-HMM) Given number of states, S, and the length of context, n, the number of contexts is S n . Long contexts → accurate modeling, but inefficient learning. Wang, et al Mining Complex Time-Series Data
  • 29. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Fixed nth-order Hidden Markov Model (n-HMM) Given number of states, S, and the length of context, n, the number of contexts is S n . Long contexts → accurate modeling, but inefficient learning. Wang, et al Mining Complex Time-Series Data
  • 30. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Fixed nth-order Hidden Markov Model (n-HMM) Given number of states, S, and the length of context, n, the number of contexts is S n . Long contexts → accurate modeling, but inefficient learning. Wang, et al Mining Complex Time-Series Data
  • 31. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Variable-length Hidden Markov Model (VLHMM) Not all contexts have to be extended to fixed length of n; Contexts have variable lengths: the shortest, but long enough to accurately determine the next state; Learning the minimum set of contexts for accurate modeling. Wang, et al Mining Complex Time-Series Data
  • 32. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Variable-length Hidden Markov Model (VLHMM) Not all contexts have to be extended to fixed length of n; Contexts have variable lengths: the shortest, but long enough to accurately determine the next state; Learning the minimum set of contexts for accurate modeling. 1 2 3 HMM Wang, et al Mining Complex Time-Series Data
  • 33. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Variable-length Hidden Markov Model (VLHMM) Not all contexts have to be extended to fixed length of n; Contexts have variable lengths: the shortest, but long enough to accurately determine the next state; Learning the minimum set of contexts for accurate modeling. 1 2 1 1 1 2 1 3 2 1 3 3 2 2 3 2 3 2 3 3 1 HMM n-HMM Wang, et al Mining Complex Time-Series Data
  • 34. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Variable-length Hidden Markov Model (VLHMM) Not all contexts have to be extended to fixed length of n; Contexts have variable lengths: the shortest, but long enough to accurately determine the next state; Learning the minimum set of contexts for accurate modeling. 1 2 1 2 2 1 2 1 1 1 1 2 1 3 2 1 3 3 3 2 1 3 2 2 2 3 2 3 3 3 2 3 3 1 3 3 3 3 HMM n-HMM VLHMM Wang, et al Mining Complex Time-Series Data
  • 35. Outline Introduction Mining by Learning Conclusion Hidden Markovian Model Various HMMs VLHMM Learning Variable-length Hidden Markov Model (VLHMM) The number of contexts is unknown before learning, even with the number of states, S, given; This situation is called “unknown model structure” in learning theory, and is the most of the four types of learning problems; As the EM algorithm cannot learn the model structure, we derived a structural-EM algorithm to learn the model; Optimizing a Minimum-Entropy criterion to learn the minimum set of contexts, and optimizing the Maximum-likelihood criterion the estimate the model parameters. Wang, et al Mining Complex Time-Series Data
  • 36. Outline Introduction Mining by Learning Conclusion Mining Patterns Contributions Mining Various Kinds of Patterns Align sequence with temporal structure The Viterbi algorithm can setup a map from each element in the sequence to a context in the graph. (Partial) Periodic Pattern Finding cyclic paths in the graph. Many algorithms are developed to do this. Search-by-Example Input the example to the Viterbi algorithm, outputs a path that is “most likely” with the example. Frequent Atomic Pattern Select those contexts that frequently appear in the training sequence. Wang, et al Mining Complex Time-Series Data
  • 37. Outline Introduction Mining by Learning Conclusion Mining Patterns Contributions Our Contribution A unified framework – mining by learning Mining from the learned temporal structure using well-studied graph algorithms; “Hidden” model support learning various kinds of sequences; Probabilistic transitions (esp, self-transitions) encode uncertainty in time-scale; Output p.d.f.s encode noises. VLHMM for efficient and accurate learning and mining Optimizing two criteria simultaneously by developing a structural-EM algorithm; Minimum-Entropy criteria → minimum number of parameters, efficient and effective learning; Maximum-Likelihood criteria → accurate learning of the temporal structure. Wang, et al Mining Complex Time-Series Data
  • 38. Outline Introduction Mining by Learning Conclusion Mining Patterns Contributions Thank You for Your Attention More details and demos can be accessed online at: http://dbgroup.cs.tsinghua.edu.cn/wangyi/vlhmm Wang, et al Mining Complex Time-Series Data

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