1. Mining Frequent Spatio-temporal Sequential Patterns
Authors: Huiping Cao, Nikos Mamoulis, David W. Cheung
Department of Computer Science, University of Hong Kong
Accepted to ICDM 2005
Abhinaya Sinha
Vijay Gandhi
CSCI 8715
Date: 4/3/06

2. Outline Introduction Problem Definition Contribution Approach
Experimental Evaluation
Assumptions
Rewrite today

3. Spatio-Temporal Pattern
Spatio-temporal sequence is a list of time-sampled locations.
(x1,y1,t1), (x2,y2,t2),…,(xn,yn,tn)
A pattern is a subset of the sequence
A pattern is frequent if its support >= threshold value
Bus routes across 3 runs

4. Motivation Predict trajectory of an object
Detect frequent routes followed by an object
Ecology
CHIMPS project at UofM (
Tracking chimpanzee movements and analyzing their behavior
Location based services
Where a user may go next and thus, provide customized services

5. Problem Definition
Input: Given spatio-temporal sequence S and support threshold min_sup
Output: Frequent spatio-temporal patterns
Objective: Lower computation time and space
Constraints: Use of a device such as GPS to sample locations

6. Contributions Model for spatio-temporal sequential pattern mining
Algorithm for extracting frequent singular spatial pattern elements a.k.a. spatial regions
Algorithm for combining single regions to patterns of longer length

7. Methodology Convert spatio-temporal sequence to set of line segments
i.e. abstract the trajectory
Detect frequent, singular regions
Combine singular patterns to longer sequences

8. Modeling the problem Aim: abstract (approximate) the trajectory
Input: original spatio-temporal sequence
Output: sequence segments
Need
locations are not repeated exactly
Derived line segments are used for defining spatial regions
Compress original data and decrease effort required in mining
Uses Douglas-Pecker (DP) algorithm for performing this step

9. Concepts in Modeling Spatio-temporal Segment
Representative line segment of a segment
Similarity between line segments
| l1.angle – l2.angle | <= θ
| l1.len – l2.len | <= length factor * max ( l1.len, l2.len)
Closeness between line segments
Distance (points belonging to line1, line2) <= ε
Mean line segment of a set of line segments
Spatial pattern element/ spatial region
Sides determined by mean line segment and average orthogonal distance
Spatio-temporal sequential pattern
Ordered sequence of spatial pattern elements
Support of a pattern
number of sequences supporting it

10. Discovering frequent singular patterns
Input: All segments representing the spatio-temporal sequence, support threshold
Output: All segments have been assigned to regions or been found as outliers.
This step constructs frequent single spatial regions
Uses similarity and closeness to assign segments to regions

11. Deriving longer patterns
Goal is to derive longer patterns from the singular frequent patterns obtained in previous step.
Input is series SR of spatial regions.
Output: Frequent patterns.
Two algorithms
Level-wise mining
Mining using substring tree

12. Example Input: r1-r2-r1-r2-r3 minsup = 2 Output candidates
r1-r2 #2; r2-r1 #1; r2-r3 #1
r # r2 #2; r3 #1
Frequent Patterns: r1-r2; r1; r2

13. Level-wise pattern mining
Apriori Algorithm
e.g. input: r1-r2-r1-r2
r1(2) r2(2)
r1-r2(2) r2-r1(1)
Output: r1; r2; r1-r2

14. Contribution: Improvements
Connectivity constraint
Closeness property
Input: r1-r2-r1-r3-r1-r2
minsup: 2
r1(3) r2(2) r3(1)
r1-r2 r2-r1 r1-r3 r3-r1 r2r3 r3r2

15. Mining using substring tree
Tree structure with each node is pattern element
The substring tree is used to help in counting long substrings
Depth first search gives substring
e.g. r1-r2-r1-r3-r1-r2

16. Validation Methodology
Computer simulations
Candidate Algorithms: Level-wise, Grid I, Grid II, Substring tree
Evaluation done on
Real-world dataset
Synthetic dataset

17. Experimental Evaluation
Substring takes least time

18. Experimental Evaluation
Extracted patterns
Comparison with grid-based approach

19. Assumptions Spatio-temporal sequence is a list of (x,y) values
Trajectory is abstracted by line segments
Closeness and similarity of line segments is defined using 2-D data constructs
Hence is only applicable to 2-D data

20. Rewrite Today Experimental evaluation on more real-life datasets
Account for noise in input data (inaccuracy of GPS data)
Explore techniques that abstract the spatial trajectory with higher accuracy

21. Any questions??