authors: shahab helmi - computer science and...
TRANSCRIPT
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A set of 𝑛 moving objects:
A grid 𝐺:
Discretizes space
A Multivariate Spatial Event Sequence 𝑀𝑉𝑆:
𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
Player1 8 12 16 16
Player2 13 15 16 14
Player3 10 9 13 13
ℎ 𝛼 : horizontal length of 𝛼, number of events in the longest subsequence of 𝛼
v 𝛼 : vertical length of 𝛼, number of subsequences in 𝛼
ℎ 𝛼 = 3, 𝑣 𝛼 = 2
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𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
Player1 8 12 16
Player3 13 13
𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
Player1 8 12 16 16
Player2 13 15 16 14
Player3 10 9 13 13
i. ℎ 𝛼 ≥ 1 𝑎𝑛𝑑 𝑣 𝛼 ≥ 1
ii. Temporal gaps are not allowed
iii. All subsequences in 𝛼 must have the same temporal length
iv. 𝑡𝑝 𝛼 ≤ 𝑇𝑃
TP = 3
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𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
Player1 8 12 16
Player3 13 13
𝑻𝟏 𝑻𝟐 𝑻𝟑
Player1 8 - 16
𝑻𝟐 𝑻𝟑 𝑻𝟒
Player1 12 16
Player3 13 13
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Player1 8 12 16
Player2 15 16 14
Player1 8 12
Player1 8 12 16
Player2 15 16 14
Player3 9 13 13
An episode 𝛼 is a frequent episode if sup(𝛼) ≥ 𝜇,
where sup(𝛼) = |𝑛𝑜 − 𝑜𝑐𝑐(𝛼)| denotes the support of 𝛼 and
𝜇 is a user-defined minimum support threshold
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Given
a multivariate spatial event sequence 𝑀𝑉𝑆 of 𝑛 moving objects,
a minimum support threshold 𝜇,
and a maximum allowed time-span 𝑇𝑃
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The problem of 𝑴𝑽𝑺 − 𝑭𝑬𝑴 is to find all frequent episodes in 𝑀𝑉𝑆
Data preprocessing using the Spatial-Apriori property:
Reducing the size of data
Reducing the number of candidates
Mining all frequent episodes using the MVS-FEM framework
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If an episode is frequent, all of its sub-episodes are frequent
If an episode is not frequent, none of its super-episodes are frequent
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Player1 8 12 16
Player2 15 16 14
Player1 8 12
If a moving object did not frequently pass aregion 𝑅, it did not frequently pass anysub-region of 𝑅 either
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μ=3
Horizontal Growth
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Player1 8 Player2 4
Player1 7 Player2 5
Player1 8
Player2 4
Player1 7
Player2 5
Vertical Growth
Player1 8
Player2 4
Player1 8 7
Player2 4 5
Player1 8 7
Player2 4 5
Apriori property
Horizontally joinable episodes
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Player1 8 7
Player1 7 9
Player1 9 3
∪ℎ∪ℎ
Player1 8 7 9
Player1 7 9 3
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At each iteration:
1. Generate all possible valid episodes by combining episodesgenerated in the Horizontal Growth step
2. Return frequent episodes
There are too many combinations
Not practical
Vertically joinable episodes
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Player1 8 7
Player2 4 5
Player1 8 7
Player3 1 6
∪𝑣Player1 8 7
Player2 4 5
Player3 1 6
Player2 4 5
Player3 1 6
Player4 9 9
∪𝑣
Player1 8 7
Player2 4 5
Player3 1 6
Player4 9 9
Generate 𝐹2 using 𝐴𝑀𝑉𝑆 − 𝐹𝐸𝑀
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Player1 8 7
Player2 4 5
Player1 8 7
Player3 1 6
Player1 8 7 9
Player1 3 8 7
Player2 4 5 4
𝐻3
𝑉3Player1 8 7 9
Player2 4 5 4
Player1 3 8 7
Player2 4 5 4
Raw
GPS positions for 16 players (8 players per team)
Captured at 200Hz
90 minutes
9 attributes:
Player #
Timestamp
Position of the player
…
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Processed
GPS positions for 14 players (7 players per team)
Captured at 1Hz
90 minutes
3 attributes:
Player #
Timestamp
Position of the player
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Parameters Symbol Default Value
Number of events sequences in 𝑀𝑉𝑆 𝑁 7
Number of events per event sequence 𝑀 2000 (seconds)
Number of grid cells |Ω| 256
Maximum time-span 𝑇𝑃 8 seconds
Minimum support 𝜇 12
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Performance evaluation measure: execution time
Symbol Default Value
𝑁 7
𝑀 2000
|Ω| 256
𝑇𝑃 8 seconds
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Symbol Default Value
𝑀 2000
|Ω| 256
𝑇𝑃 8 seconds
𝜇 12
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Symbol Default Value
𝑁 7
𝑀 2000
|Ω| 256
𝜇 12
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Trajectory query processing
Frequent pattern mining
Sport analytics
Models for trajectory pattern mining
Activity recognition from
a single trajectory
Guessing the transportation mode
multiple trajectories
“Chasing" behavior
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Transactional Data:
Frequent itemset mining (order does not matter)
Frequent sequence mining (order matters)
Non-transactional data:
Frequent episode mining from
simple event sequences
complex event sequences
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𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
A B C A
𝑻𝟏 𝑻𝟐 𝑻𝟑 𝑻𝟒
A,B A,C C,D C,F
Sport Analytics
Predicting the next move in basketball
Predicating the location of next shot in tennis
Assessing the team formation in soccer
Player analysis
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Conclusion
Introduced the co-movement pattern
Introduced the “Spatial Apriori” property
Proposed a preprocessing technique based on the Spatial Apriori property
Introduced the MVS-FEM framework
Proposed 3 algorithms for the MVS-FEM problem
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