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Multiscale Frequent Co-movement Pattern Mining ICDE 2020 - 04/22/2020 Authors: Shahab Helmi , shahab.helmi@ucdenver.edu Farnoush Banaei-Kashani, farnoush.banaei-kashani@ucdenver.edu Frequent Co-Movement Patterns (F-CoMP) 2 Movements of

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SLIDE 1

Multiscale Frequent Co-movement Pattern Mining

ICDE 2020 - 04/22/2020

Authors:

Shahab Helmi, shahab.helmi@ucdenver.edu Farnoush Banaei-Kashani, farnoush.banaei-kashani@ucdenver.edu

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SLIDE 2

2 Frequent Co-Movement Patterns (F-CoMP)

Movements of multiple objects at the same time

  • Objects do not need to spatially close to each other
  • Movements can have different shapes

Frequent?

  • Strategy of team
  • Mobility disorder
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SLIDE 3

3 Related Work

Pattern Query Spatial Proximity Frequent Temporal Multi-object Track, Leadership [1] Y Y

  • N

Y Y Constance, Convergence, Concurrence, Meet [2] N Y Y N Y Y Trajectory Clustering [3] N Y Y N N Y Flock [4], Convoy [5], Swarm [6], Traveling Companions [7] N Y Y N Y Y Co-location [8] N Y Y Y N Y Co-location Episodes [9], Co- Occurrence [10], Mix-drove [11] N Y Y Y Y Y Frequent Periodic Movements [12] N Y Y Y Y N Frequent Complex Episodes [13] N N

  • Y

Y Y Closed Multi-sequence Series [14] N N

  • Y

Y Y Frequent Co-movement Patterns N Y N Y Y Y

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SLIDE 4

4 Co-Movement Pattern Representation Definition

๐‘ž = ๐‘1 ๐‘”

11

๐‘”

12

๐‘2 ๐‘”

21

๐‘”

22

โ€ฆ ๐‘”

1๐‘™

โ€ฆ ๐‘”

2๐‘™

โ‹ฎ โ‹ฎ ๐‘๐‘œ ๐‘”

๐‘œ1

๐‘”

๐‘œ2

โ‹ฎ โ‹ฎ โ‹ฏ ๐‘”

๐‘œ๐‘™

where ๐‘”

๐‘—๐‘˜ is one or more spatial features

  • direction
  • acceleration
  • displacement
  • distance traveled
  • โ€ฆ

๐‘ž = ๐‘1 โ†’ โ†’ ๐‘2 โˆ’ โ†’ sup(๐‘ž) = 5

  • sup ๐‘ž โ‰ฅ ๐‘ก๐‘ฃ๐‘ž๐‘›๐‘—๐‘œ
  • ๐‘‹

๐‘›๐‘๐‘ฆ

Movement pattern In this paper

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SLIDE 5

5 Problem Statement

Mining all F-CoMPs is challenging:

  • ฯƒ๐‘œ=1

|๐‘ƒ| ฯƒ๐‘™=2 ๐‘‹

๐‘›๐‘๐‘ฆ |๐‘ƒ|

๐‘œ

ร—

๐‘‹

๐‘›๐‘๐‘ฆ

๐‘™

ร— ๐‘ˆ possible CoMPs

  • Given |๐‘ƒ| = 10, ๐‘‹

๐‘›๐‘๐‘ฆ = 10, ๐‘ˆ = 100 โ‡’ >103M

  • Given |๐‘ƒ| = 20, ๐‘‹

๐‘›๐‘๐‘ฆ = 10, ๐‘ˆ = 100 โ‡’ >16B

Given ๐ธ, ๐‘ก๐‘ฃ๐‘ž๐‘›๐‘—๐‘œ, and ๐‘‹

๐‘›๐‘๐‘ฆ

Our goal is to mine all F-CoMPs from ๐ธ

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SLIDE 6

6 Outline

โœ“Introduction โœ“Related Work โœ“Problem Definition

  • Solution
  • Frequent Movement Pattern Mining
  • Frequent Co-Movement Pattern Mining
  • Multiscale Frequent Co-Movement Pattern Mining
  • Experimental Results
  • Conclusions & Future Work
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SLIDE 7

7 F-CoMP Mining: Baseline Solution

Mine frequent movement patterns (F-MP) Generate F-CoMPs by efficiently joining F-MPs

๐‘ž1 = ๐‘ƒ2 โ†’ โ†’ ๐‘ž3 = ๐‘ž1 + ๐‘ž2 = ๐‘ƒ2 โ†’ โ†’ ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž1

โ€ฒ = ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ž2

โ€ฒ = ๐‘ƒ3 โ†‘

โ†‘ โ† ๐‘ž2 = ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž3

โ€ฒ = ๐‘ž1 โ€ฒ + ๐‘ž2 โ€ฒ = ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ƒ3 โ†‘ โ†‘ โ† Iteration Iteration 1 Iteration 2

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SLIDE 8

8 Movement Pattern Mining

Mine frequent movement patterns (F-MP) โ†’ Extension instead of generation Generate F-CoMPs by efficiently joining F-MPs

๐‘ž1 = ๐‘ƒ2 โ†’ โ†’ ๐‘ž3 = ๐‘ž1 + ๐‘ž2 = ๐‘ƒ2 โ†’ โ†’ ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž1

โ€ฒ = ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ž2

โ€ฒ = ๐‘ƒ3 โ†‘

โ†‘ โ† ๐‘ž2 = ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž3

โ€ฒ = ๐‘ž1 โ€ฒ + ๐‘ž2 โ€ฒ = ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ƒ3 โ†‘ โ†‘ โ† Iteration Iteration 1 Iteration 2

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SLIDE 9

9 Extending Movement Patterns

Basic apriori algorithm:

  • kth iteration:
  • For each k-movement identify the

joinable k movements

  • For each joinable pair, compute support
  • O( ๐‘๐‘™ 2 ร— avg(sup( ๐‘๐‘™)))

Joinable if share a k-1 items Extension method:

  • Extend each occurrence using the

trajectory

  • O( ๐‘๐‘™ ร— avg(sup( ๐‘๐‘™)))
  • avg(sup( ๐‘๐‘™) โ‰ช |๐‘๐‘™|

๐‘ž1 {โ†’ โ†’ โ†‘} 3 โ†’ โ†‘ โ†’ {โ†’ โ†’ โ†‘ โ†’} 2 {โ†’ โ†’ โ†‘ โ†‘ } 1 ๐‘ž1 {โ†’ โ†’ โ†‘} ๐‘ž2 {โ†’ โ†‘ โ†‘} ๐‘ž3 {โ†“ โ†“ โ†’} {โ†’ โ†’ โ†‘ โ†‘ }

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SLIDE 10

10 Frequent Gapped Movement Pattern

  • More movements
  • Different measures for computing

the support

  • Head-frequency [15]
  • Not monotonic
  • All possible movements must be

generated for each window .

  • Then head-frequency once must be

identified.

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SLIDE 11

11 F-CoMP Mining

Mine frequent movement patterns (F-MP) Generate F-CoMPs by efficiently joining F-MPs

๐‘ž1 = ๐‘ƒ2 โ†’ โ†’ ๐‘ž3 = ๐‘ž1 + ๐‘ž2 = ๐‘ƒ2 โ†’ โ†’ ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž2 = ๐‘ƒ3 โ†‘ โ†‘

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SLIDE 12

12 F-CoMP Mining

  • We already have frequent k movement patterns (๐‘๐‘™)
  • Naรฏve approach:
  • Generate all possible combinations using the frequent k movement patterns
  • ฯƒ๐‘™=2

๐‘‹

๐‘›๐‘๐‘ฆ ฯƒ๐‘œ=2

|๐‘ƒ| |๐‘๐‘™| ๐‘œ

  • Compute support for each combination
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SLIDE 13

13 Basic Apriori for F-CoMP Mining

  • Generate the F-CoMPs with ๐‘œ + 1 objects from the F-CoMPs with ๐‘œ
  • bjects
  • Find joinable patterns
  • F-CoMPs that have ๐‘œ โˆ’ 1 movement patterns in common are joinable
  • ฯƒ๐‘™=2

๐‘‹

๐‘›๐‘๐‘ฆ |๐บ

๐‘™,๐‘œ |2

  • Compute support

๐‘ž1 = ๐‘2 โ†’ โ†’ โ†’

  • 3

โ†‘ โ†‘ โ†‘

  • 4

โ† โ† โ† ๐‘ž3 = ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘7 โ†“ โ†“ โ†“ ๐‘ž1 + ๐‘ž3 = ๐‘2 ๐‘3 โ†’ โ†’ โ†’ โ†‘ โ†‘ โ†‘ ๐‘4 ๐‘7 โ† โ† โ† โ†“ โ†“ โ†“

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SLIDE 14

14 Improving the Search for Joinable Patterns

b1 (o2, o3, o4) ๐‘ž1 = ๐‘2 โ†’ โ†’ โ†’

  • 3

โ†‘ โ†‘ โ†‘

  • 4

โ† โ† โ† ๐‘ž2 = ๐‘2 โ† โ† โ† ๐‘3 โ†’ โ†’ โ†’ ๐‘4 โ†‘ โ†‘ โ†‘ b3 (๐‘3, ๐‘8, o10) ๐‘ž5 = ๐‘4 โ† โ† โ† ๐‘5 โ† โ† โ† ๐‘6 โ† โ† โ† ๐‘ž6 = ๐‘4 โ† โ† โ† ๐‘5 โ† โ† โ† ๐‘6 โ† โ† โ† ๐‘ž5 = ๐‘4 โ† โ† โ† ๐‘5 โ† โ† โ† ๐‘6 โ† โ† โ† ๐‘2 (๐‘2, o3, o7) ๐‘ž3 = ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘7 โ†“ โ†“ โ†“ ๐‘ž4 = ๐‘2 โ† โ† โ† ๐‘3 โ† โ† โ† ๐‘7 โ† โ† โ†

Objects Buckets (๐‘2, ๐‘3) ๐‘1 (๐‘2, ๐‘4) ๐‘1 (๐‘3, ๐‘4) ๐‘1 Objects Buckets (๐‘2, ๐‘3) ๐‘1, ๐‘2 (๐‘2, ๐‘4) ๐‘1 (๐‘3, ๐‘4) ๐‘1 (๐‘2, ๐‘7) ๐‘2 (๐‘3, ๐‘7) ๐‘2 Objects Buckets (๐‘2, ๐‘3) ๐‘1, ๐‘2 (๐‘2, ๐‘4) ๐‘1 (๐‘3, ๐‘4) ๐‘1 (๐‘2, ๐‘7) ๐‘2 (๐‘3, ๐‘7) ๐‘2 (๐‘3, ๐‘8) ๐‘3 โ€ฆ โ€ฆ

First look for joinable buckets rather than joinable patterns

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SLIDE 15

15 Improving the Search for Joinable Patterns (contโ€™d)

Look for joinable patterns only in the joinable buckets

b1 (o2, o3, o4)

๐‘ž1 = ๐‘2 โ†’ โ†’ โ†’

  • 3

โ†‘ โ†‘ โ†‘

  • 4

โ† โ† โ† ๐‘ž2 = ๐‘2 โ† โ† โ† ๐‘3 โ†’ โ†’ โ†’ ๐‘4 โ†‘ โ†‘ โ†‘

๐‘2 (๐‘2, o3, o7)

๐‘ž3 = ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘7 โ†“ โ†“ โ†“ ๐‘ž4 = ๐‘2 โ† โ† โ† ๐‘3 โ† โ† โ† ๐‘7 โ† โ† โ† Objects Buckets

(๐‘2, ๐‘3) ๐‘1, ๐‘2 Objects Patterns ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘ž1, ๐‘ž3 ๐‘2 โ† โ† โ† ๐‘3 โ†’ โ†’ โ†’ ๐‘ž2 ๐‘2 โ† โ† โ† ๐‘3 โ† โ† โ† ๐‘ž4

๐‘ž1 + ๐‘ž3 = ๐‘2 ๐‘3 โ†’ โ†’ โ†’ โ†‘ โ†‘ โ†‘ ๐‘4 ๐‘7 โ† โ† โ† โ†“ โ†“ โ†“ เท

๐‘™=2 ๐‘‹

๐‘›๐‘๐‘ฆ

เท

๐‘œ=2 |๐‘ƒ|

๐ถ๐‘™ + ๐‘๐‘™ ๐‘๐‘ค๐‘• เท

๐‘™=2 ๐‘‹

๐‘›๐‘๐‘ฆ

เท

๐‘œ=2 |๐‘ƒ|

|๐บ

๐‘™, ๐‘œ แ‰š 2 Objects Patterns ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘ž1

๐‘2 โ† โ† โ† ๐‘3 โ†’ โ†’ โ†’ ๐‘ž2

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SLIDE 16

16 F-CoMP Extension

Mine frequent movement patterns (F-MP)

  • Horizontal Extension

Generate F-CoMPs by efficiently joining F-MPs

  • Vertical Extension

๐‘ž1 = ๐‘ƒ2 โ†’ โ†’ ๐‘ž3 = ๐‘ž1 + ๐‘ž2 ๐‘ƒ2 โ†’ โ†’ ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž1

โ€ฒ = ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ž2

โ€ฒ = ๐‘ƒ3 โ†‘

โ†‘ โ† ๐‘ž2 = ๐‘ƒ3 โ†‘ โ†‘ ๐‘ž3

โ€ฒ = ๐‘ž1 โ€ฒ + ๐‘ž2 โ€ฒ ๐‘ƒ2 โ†’

โ†’ โ†‘ ๐‘ƒ3 โ†‘ โ†‘ โ† Iteration 1 Iteration 2

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SLIDE 17

17 Extension Rather than Generation

๐บ

3,3

๐‘ž1 = ๐‘2 โ†’ โ†’ โ†’

  • 3

โ†‘ โ†‘ โ†‘

  • 4

โ† โ† โ† ๐‘ž2 = ๐‘2 โ†’ โ†’ โ†’ ๐‘3 โ†‘ โ†‘ โ†‘ ๐‘4 โ†’ โ†’ โ†’

๐บ

4

๐‘›1 = { ๐‘2 โ†’ โ†’ โ†’ โ†‘ } ๐‘›2 = { ๐‘3 โ†‘ โ†‘ โ†‘ โ†’ } ๐‘›3 = { ๐‘4 โ†“ โ† โ† โ† }

เท

๐‘™=2 ๐‘‹

๐‘›๐‘๐‘ฆ

เท

๐‘œ=2 |๐‘ƒ|

|๐บ

๐‘™,๐‘œ แ‰š 2

๐‘ž1

โ€ฒ =

๐‘2 โ†’ โ†’ โ†’ โ†‘ ๐‘3 โ†‘ โ†‘ โ†‘ โ†’ ๐‘4 โ†“ โ† โ† โ† เท

๐‘œ=2 |๐‘ƒ|

๐ถ2 + ๐‘2 ๐‘๐‘ค๐‘• + เท

๐‘™=3 ๐‘‹

๐‘›๐‘๐‘ฆ

เท

๐‘œ=2 |๐‘ƒ|

|๐บ

๐‘™, ๐‘œ|

เท

๐‘™=2 ๐‘‹

๐‘›๐‘๐‘ฆ

เท

๐‘œ=2 |๐‘ƒ|

|๐บ

๐‘™|

๐‘œ

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SLIDE 18

18 Outline

โœ“Introduction โœ“Related Work โœ“Problem Definition

  • Solution

โœ“Frequent Movement Pattern Mining โœ“Frequent Co-Movement Pattern Mining

  • Multiscale Frequent Co-Movement Pattern Mining
  • Experimental Results
  • Conclusions & Future Work
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SLIDE 19

19 Scale (Resolution) and Density Reachable Movements

๐‘ž = ๐‘ƒ2 โ†’ โ†’ sup(๐‘ž) = 5 ๐‘ž1

๐‘ก1 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž1

๐‘ก1) = 1

๐‘ž3

๐‘ก1 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž3

๐‘ก1) = 3 s1

supmin = 2 s2

๐‘ž1

๐‘ก1 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž1

๐‘ก1) = 1

Multiscale analysis!

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SLIDE 20

20 Scale (Resolution) and Density Reachable Movements

supmin = 2 s2

๐‘ž3

๐‘ก1 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž3

๐‘ก1) = 3

๐‘ž1

๐‘ก2 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž3

๐‘ก1) = 2

๐‘ž2

๐‘ก2 = ๐‘ƒ2 โ†’ โ†’

sup(๐‘ž3

๐‘ก1) = 1

Scale only applies on movements, not co-movements โ‡’ different object can still be far from each other

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SLIDE 21

21 Experimental Setup

Soccer dataset [16]

  • 10 players (excluded goalkeeper)
  • 90 minutes at 1Hz

Gait dataset [17]

  • 100 subjects
  • 30 walks x 20 joints at 1Hz

Evaluation Metrics:

  • Execution time
  • Memory footprint
  • Generated candidates

Implementation:

  • .NET Core (C#)

Workstation:

  • Intel Core-i7 3.6GHz CPU
  • 16GB of RAM

Parameters Soccer Gait The number of objects |๐‘ƒ| 10 30 Frame per second FPS 1 1 Scale ๐‘ก 5m 3cm Max window size ๐‘‹

m๐‘๐‘ฆ

12 and 8 6 Minimum support ๐‘‡๐‘ฃ๐‘ž๐‘›๐‘—๐‘œ 8 and 4 4 Directions |๐‘’| 12 12

Please refer to the paper to see all the experiments โ˜บ We used logarithmic scale for the values on Y axis

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SLIDE 22

22

Related Work Comparison: F-CoMP Miner vs. PIE+ [13]

1 10 100 1,000 10,000 100,000 1,000,000 1 2 3 4 5 6 7 8 9 10 Execution Time (sec) Number of Objects 1 10 100 1000 10000 6 8 10 12 14 16 Execution Time (sec) Maximum Window Size

F-CoMP PIE+,|O|=10 PIE+,|O|=2 PIE+,|O|=3

PIE+ is very memory efficient

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SLIDE 23

23 F-CoMP Mining Results: Soccer Dataset

3,174 1 10 100 1,000 10,000 3 4 5 6 7 8 Minimum Support Memory (MB) Time (sec) 1 100 10,000 1,000,000 100,000,000 10,000,000,000 3 4 5 6 7 8 Count Minimum Support Naive CoMPs CoMPs F-CoMPs

slide-24
SLIDE 24

24 Multiscale F-CoMP Miner

1 10 100 1000 10000 24 48 72 96 120 144 168 192 Execution Time (sec) Number of Scales Mining Patterns Deriving Patterns

s1 s2 s3

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SLIDE 25

25 Conclusions

  • Defined co-movement patterns
  • Proposed efficient solutions for multiscale movement and co-movement

pattern mining

  • Evaluated our solutions with 2 real datasets
  • Reduced the number of generated CoMPs up to 50,000 times for the

soccer dataset and even more for the gate dataset

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SLIDE 26

26 Future Work

Subject 1 Subject 2

Each cell shows the % of F-CoMPs that includes both of the corresponding joints

Hypothesis: using F-CoMPs for classification

Joint ID Joint ID Joint ID Joint ID

slide-27
SLIDE 27

Thank You!

Q&A

slide-28
SLIDE 28

28 References

[1] Laube, Patrick, Marc van Kreveld, and Stephan Imfeld. "Finding REMOโ€”detecting relative motion patterns in geospatial lifelines." Developments in spatial data handling. Springer, Berlin, Heidelberg, 2005. 201-215. [2] Gudmundsson, Joachim, Marc van Kreveld, and Bettina Speckmann. "Efficient detection of motion patterns in spatio-temporal data sets." Proceedings of the 12th annual ACM international workshop on Geographic information

  • systems. 2004.

[3] Lee, Jae-Gil, Jiawei Han, and Kyu-Young Whang. "Trajectory clustering: a partition-and-group framework." Proceedings of the 2007 ACM SIGMOD international conference on Management of data. 2007. [4] Benkert, Marc, et al. "Reporting flock patterns." Computational Geometry 41.3 (2008): 111-125. [5] Orakzai, Faisal, Toon Calders, and Torben Bach Pedersen. "k/2-hop: fast mining of convoy patterns with effective pruning." Proceedings of the VLDB Endowment 12.9 (2019): 948-960. [6] Li, Zhenhui, et al. "Swarm: Mining relaxed temporal moving object clusters." Proceedings of the VLDB Endowment 3.1-2 (2010): 723-734. [7] Tang, Lu-An, et al. "A framework of traveling companion discovery on trajectory data streams." ACM Transactions on Intelligent Systems and Technology (TIST) 5.1 (2014): 1-34.

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SLIDE 29

29 References (contโ€™d)

[8] Wu, Pingping, et al. "UMine: Study on Prevalent Co-locations Mining from Uncertain Data Sets." International Conference on Geo-Spatial Knowledge and Intelligence. Springer, Singapore, 2017. [9] Cao, Huiping, Nikos Mamoulis, and David W. Cheung. "Discovery of periodic patterns in spatiotemporal sequences." IEEE Transactions on Knowledge and Data Engineering 19.4 (2007): 453-467. [10] Celik, Mete. "Partial spatio-temporal co-occurrence pattern mining." Knowledge and Information Systems 44.1 (2015): 27-49. [11] Celik, Mete, et al. "Mixed-drove spatiotemporal co-occurrence pattern mining." IEEE Transactions on Knowledge and Data Engineering 20.10 (2008): 1322-1335. [12] Cao, Huiping, Nikos Mamoulis, and David W. Cheung. "Discovery of collocation episodes in spatiotemporal data." Sixth International Conference on Data Mining (ICDM'06). IEEE, 2006. [13] Huang, Kuo-Yu, and Chia-Hui Chang. "Efficient mining of frequent episodes from complex sequences." Information Systems 33.1 (2008): 96-114. [14] Lee, Anthony JT, et al. "Mining closed patterns in multi-sequence time-series databases." Data & Knowledge Engineering 68.10 (2009): 1071-1090.

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SLIDE 30

30 References (contโ€™d)

[15] Iwanuma, Koji, Yo Takano, and Hidetomo Nabeshima. "On anti-monotone frequency measures for extracting sequential patterns from a single very-long data sequence." IEEE Conference on Cybernetics and Intelligent Systems, 2004.. Vol. 1. IEEE, 2004. [16] Pettersen, Svein Arne, et al. "Soccer video and player position dataset." Proceedings of the 5th ACM Multimedia Systems Conference. 2014. [17] http://cse.ucdenver.edu/~bdlab/datasets/gait/index.html