Transcript of "A Unified Approach to Mining Complex Time-Series Data for ..."
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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