Probabilistic Similarity Search for Uncertain Time SeriesPresented by CAO Chen21st Feb, 2011

Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

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Background – Time Series

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Background – Time Series (cont’d)• Source of Time Series Data• Traffic measurements

• Uncorrelated

• Location tracking of moving objects

• Measuring environmental parameter(temperature)• Correlated 4

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Background – Similarity Search• Similarity Search• Pattern Matching• Shape Matching

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Background – Similarity Search (cont’d)• Range Query• Return all tuples that fits between an upper and lower boundary. • We don’t know how many it will return• Slower than top-k because no upper bound to prune

• Sequence Matching• Whole matching: Sequences with same length• Subsequence Matching

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Motivation & Contribution• Uncertainty • Moving objects• Object identification• Sensor network monitoring

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Motivation & Contribution (cont’d)• Contribution• (Firstly) Formalize the notion of uncertain time series• Two novel types of probabilistic range queries over uncertain

time series• Pruning strategy based on approximating representation of

uncertainty• Explicitly evaluate the refinement(processing) time cost

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Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

CAO

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Probabilistic Queries Over Uncertain TS• Definition of Uncertain Time Series

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Probabilistic Queries Over Uncertain TS (cont’d)• Definition of Uncertain Lp-Distance

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Probabilistic Queries Over Uncertain TS (cont’d)• Definition of Probabilistic Range Queries

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Challenge in Processing Range Queries with Uncertainty• Naïve Solution

• Computing all distance observations• CPU-bound vs. I/O bound• Long time series and high sample rates (large n), • Naïve Solution• Number of computing the distance

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Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

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Approximate Representation

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Approximate Representation (cont’d)• Two Levels of Appr. Representation• Different in whether existing multiple(K) groups of sample

observation in one time slot

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By K-means clusteringOnly one group at each time slot

Distance Approximations

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Distance Approximations (cont’d)

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Distance Approximations (cont’d)• Lemma 1

• Lemma 2

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Probabilistic Bounded Range Queries (PBRQ)

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True Hit

True Drop

Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

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Step-Wise Refinement• When to refine?• Time series that could not be filtered or determined simply by

comparing the interval of lower and upper bound• Refinement Goal• To identify an uncertain time series as true hit or true drop

• Condition to increase the lower bound

• Increase of the number of qualified distance

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Step-Wise Refinement (cont’d)

• Refinement heuristics

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Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

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Evaluation• Benchmark• UCI Time Series Data Mining Archive• CBF, GUN/POINT, CONTROL CHART, OSU LEAF

• Uncertainty• Generating samples uniformly distributed around the given exact

values

• Evaluation• Overall Speed-Up• Refinement Speed-Up

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Evaluation (cont’d)• Speed-up for Probabilistic Bounded Range Query (PBRQ)

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Evaluation (cont’d)• Speed-up for Probabilistic Rank Range Query (PRRQ)

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Evaluation (cont’d)• Speed-up w.r.t. scalability

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Evaluation (cont’d)• Refinement• S-S: using proposed strategy• R-R: randomly processing for both steps

• Logarithm value of required calculations

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Outline• Introduction• Background• Time Series• Similarity Search

• Motivation & Contribution• Uncertain Time Series Query • Uncertainty Approximation• Step-wise Refinement

• Evaluation• Related Literature Review• Q & A

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B G

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Q & A

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• Thank You