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1
Fair Use Agreement

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• (c) Eamonn Keogh, eamonn_at_cs.ucr.edu

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Indexing Large Human-Motion Databases

• Eamonn Keogh, Themis Palpanas Victor B.
  Zordan,Dimitrios Gunopulos
• University of California, Riverside
• Marc Cardle
• University of Cambridge

3
Motion Capture

• records motion data from live actors

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Motion Capture

• records motion data from live actors
• used for data-driven animation

5
Motion Capture in Games Industry
Street NBA
Madden
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Motion Capture in Movie Industry
Troy
Lord of the Rings
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Motivation

• motion capture data
• segmented in short sequences, stored in motion
  libraries
• composed to create long, realistic motion
  sequences
• important to find similar sequences
• form pool of similar sequences
• choose the most promising, to continue the motion

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Motivation

• Dynamic Time Warping (DTW)
• Considers only local adjustments in time, to
  match two time series
• However sometimes global adjustments are required
• DTW is being extensively used
• uniform scaling is complementary
• combination of both techniques offers rich,
  high-quality result set

Uniform Scaling
DTW
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Uniform Scaling

• time series
• query, Q, length n
• candidate, C, length m (mgtn)

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Uniform Scaling

• time series
• query, Q, length n
• candidate, C, length m (mgtn)
• stretch Q to length p (npm) Qp
• Qpj Qjn/p, 1 j p
• scaling factor, sf p/n
• max scaling factor, sfmax m/n

Qp
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Problem Statement

• given
• time series, Q
• database of candidate time series, D
• find argminp dist(Qp, D )
• dist(Qp, D ) Euclidean Distance between time
  series

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Problem Statement

• given
• time series, Q
• database of candidate time series, D
• find argminp dist(Qp, D )
• dist(Qp, D ) Euclidean Distance between time
  series

• challenges
• quickly solve the problem for two time series
• extend solution to scale-up to large time series
  databases

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Outline

• Speeding Up Search
• Scaling Up To Large Databases
• Experimental Evaluation
• Related Work
• Conclusions

14
Best Uniform Scaling Match

• brute force algorithm
• for each time series in D
• for each sf, 1 sf sfmax
• compute distance between the two time
  series
• find the best overall match
• time complexity O(D(m-n))
• extremely expensive!

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Lower Bounding Uniform Scaling

• lower bound distance between two time series,
• for any sf, 1 sf sfmax
• desiderata
• fast to compute
• tight bound
• results in fast pruning of candidates that are
  guaranteed not to belong to the solution
• compute distance only for time series not pruned
  by lower bound

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Lower Bounding Uniform Scaling

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100

C
m 100
0
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Lower Bounding Uniform Scaling

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100
• build envelopes, length 80

U
n 80
Ui max( C ?(i-1)m/n? 1,, C ?im/n? )
Li min( C ?(i-1)m/n? 1,, C ?im/n? )
L
0
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Lower Bounding Uniform Scaling
Q

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100
• build envelopes, length 80

Ui max( C ?(i-1)m/n? 1,, C ?im/n? )
Li min( C ?(i-1)m/n? 1,, C ?im/n? )
0
10
20
30
40
50
60
70
80
90
100
19
Lower Bounding Uniform Scaling

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100
• build envelopes, length 80

Ui max( C ?(i-1)m/n? 1,, C ?im/n? )
Li min( C ?(i-1)m/n? 1,, C ?im/n? )
0
10
20
30
40
50
60
70
80
90
100
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Lower Bounding Uniform Scaling

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100
• compute lower bound

0
10
20
30
40
50
60
70
80
90
100
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Envelope Indexing

• dimensionality of envelopes is high

80 points
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Envelope Indexing

• dimensionality of envelopes is high
• reduce dimensionality by approximating them
• Piecewise Constant Approximation

8 points
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Envelope Indexing

• dimensionality of envelopes is high
• reduce dimensionality by approximating them
• Piecewise Constant Approximation
• assume query Q, length 80

Q
0
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40
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80
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Envelope Indexing

• dimensionality of envelopes is high
• reduce dimensionality by approximating them
• Piecewise Constant Approximation
• assume query Q, length 80
• we approximate it with 8 points

0
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Envelope Indexing

• dimensionality of envelopes is high
• reduce dimensionality by approximating them
• Piecewise Constant Approximation
• assume query Q, length 80
• approximated with 8 points
• compute approximation of
• lower bound

0
10
20
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40
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Algorithms for Secondary Storage

• use a multidimensional index
• VA-file -gt FastScan algorithm
• R-tree -gt RtreeProbe algorithm
• 2-pass algorithms
• 1. scan approximated envelopes,
• prune search space
• 2. find exact answer using original series

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Outline

• Speeding Up Search
• Scaling Up To Large Databases
• Experimental Evaluation
• Related Work
• Conclusions

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Datasets Used

• motion capture
• data from 124 sensors placed on human actors
• mixed bag
• time series coming from
• medicine, manufacturing, environmental
  monitoring, economics, sensor data
• experimented with time series databases of
• size 5,000 80,000
• time series length 64 1,024 points

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Main Memory Experiments

• assume database fits in memory
• measure pruning power
• fraction of times each approach calls distance
  function
• our technique
• 1 order of magnitude
• faster than CD-criterion

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Main Memory Experiments
brute force

• assume database fits in memory
• measure pruning power
• fraction of times each approach calls distance
  function
• our technique
• 1 order of magnitude
• faster than CD-criterion
• 3 orders of magnitude
• faster than brute force

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Disk-Based Experiments

• comparison of
• brute force
• FastScan
• RtreeProbe

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Disk-Based Experiments

• comparison of
• FastScan
• RtreeProbe

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Disk-Based Experiments

• comparison of
• FastScan
• RtreeProbe

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Case Study

• video

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Outline

• Speeding Up Search
• Scaling Up To Large Databases
• Experimental Evaluation
• Related Work
• Conclusions

36
Related Work

• Dynamic Time Warping (DTW)
• Yi Faloutsos00Keogh02Zhu
  Shasha03Fung Wong03
• Longest Common SubSequence (LCSS)
• Das et al.97Vlachos et al.03
• uniform scaling
• Argyros Ermopoulos03

37
Outline

• Speeding Up Search
• Scaling Up To Large Databases
• Experimental Evaluation
• Related Work
• Conclusions

38
Conclusions

• studied utility of uniform scaling similarity
  matching
• applications in
• motion capture libraries, music retrieval,
  historical handwritten archives
• introduced first lower bounding technique
• proposed indexing method for bounding envelopes
• suitable for very large time series databases
• experimentally evaluated efficiency of technique
• demonstrated quality of results with real motion
  capture data

39
Outline
40
Lower Bounding Uniform Scaling

• assume
• candidate C, length 100
• query Q, length 80
• wish to find best match for any
• scaling of Q between 80-100
• build envelopes, length 80

Ui max( C ?(i-1)m/n? 1,, C ?im/n? )
Li min( C ?(i-1)m/n? 1,, C ?im/n? )
0
10
20
30
40
50
60
70
80
90
100