Chris Andrews

1
Trajectory Pattern Mining
Fosca Giannotti
Dino Pedreschi
Mirco Nanni
Fabio Pinelli
Chris Andrews
Georgia Institute of Technology B.S. Computer
Science 5th Year Undergraduate
2
Concepts

• Analyze trajectory of moving objects
• A 3mins B 5mins C 10mins
  D
• Trajectory Patterns description of frequent
  behavior relating to space and time
• Frequent Sequence Pattern (FSP)
• Determine if trajectory sequence matches any
  trajectory patterns in a given set
• Study different methods of preparing a Temporally
  Annotated Sequence (TAS) for data mining

3
Trajectory Patterns (T-Patterns)

• Trajectory Pattern
• sequence of time-stamped locations
• S ( x0, y0, t0 ) , , ( xn, yn, tn )
• Temporal Annotation
• set of times relating to trajectories
• A a1 , a2, an
• Temporally Annotated Sequence
• (S,A) (x0,y0) a1 (x1,y1) a2 an
  (xn,yn)

4
Neighborhood Function

• Neighborhood Function N R2 -gt P (R2)
• Calculates spatial containment of regions
• Input point to find enclosing Region of Interest
• Defines the necessary proximity to fall into a
  region
• Parameters
• e radius or necessary proximity of points

5
Regions of Interest (RoI)

• Performing these comparisons on points is costly
• A simple preprocessing step can alleviate this
• Utilize the Neighborhood Function NR()
• Translate each set of points into regions
• Timestamp is selected from when the trajectory
  first entered the region
• Now compare sequence of regions and timestamps
  using the TAS mining algorithm presented in 2.

6
Static RoI

• Neighborhood Function NR()
• Initially receives set of R disjoint spatial
  regions
• R regions are predefined based on prior knowledge
• Each represents relevant place for processing
• Static NR() simplifies problem of mining patterns
• Sequence of points become grouped
• Result sequence of regions
• (x,y) a1 (x,y) becomes X a1 Y

7
Dynamic RoI

• Data sets often do not possess predetermined
  regions
• Instead need to formulate regions based on
  criteria of density of the trajectories
• Preprocessing now must determine set R of popular
  regions from the data set
• R is now the set of Region of Interests from used
  by the Neighborhood Function NR() to translate
  points into Regions of Interest

8
Popular Regions

• Grid G of n x m cells Density Threshold d
• Each cell with density G(i,j) Set R of
  popular regions
• Each region in R forms rectangular region
• Sets in R are pair wise distinct
• Dense cells always contained in some region in R
• All regions in R have average density above d
• All regions in R cannot expand without their
  average density decreasing below d

9
Grid Density Preparation

• Split space into n x m grid with small cells
• Increment cells where trajectory passes
• Neighborhood Function NR() determines which
  surrounding cells
• Regression - increment continuously along
  trajectory

10
Popular Regions Algorithm

• Algorithm PopularRegions( G, d )
• Complexity O ( G log G )
• Iteratively consider each dense cell
• For each
• Expands in all four directions
• Select expansion that maximizes density
• Repeat until expansion would decrease below
  density threshold

11
Results
12
Evaluating the T-Patterns

• Compute density of each cell of grid
• Compute set of RoIs by determining Popular
  Regions
• Translate the input trajectories into sequence of
  RoIs and timestamps for the transitions
• Input the trajectories and times into TAS mining
  algorithm2

13
Experiments

• GPS Data
• Fleet of 273 trucks in Athens, Greece
• 112,203 total points recorded
• Running both static dynamic pattern algorithms
• Various parameter settings
• Performance Analysis
• Synthetic Data by CENTRE synthesizer
• 50 random 50 predetermined

14
Pattern Mining Results
Static found A t1 B t2
B Dynamic found A t1 B t2 B
15
Execution Time Results

• Increase linearly with increasing number of input
  trajectories (both algorithms)
• Grow when density threshold decreases
• Static performs better with extreme threshold
• Static does not perform with middle threshold

16
Additional Results

• Increasing radius of spatial neighborhood obtains
  irregular performance and large values lead to
  poor execution times
• Changing time tolerance (t) obtains results
  similar to TASs
• Increasing the number of points in each
  trajectory causes linear growth of execution times

17
Works Cited

• 1 Trajectory pattern mining, Fosca Giannotti,
  Mirco Nanni, Fabio Pinelli, Dino Pedreschi,
  Proceedings of the 13th ACM SIGKDD international
  conference on Knowledge discovery and data mining
  KDD. ACM, 2007.
• 2 Efficient Mining of Sequences with Temporal
  Annotations. F. Giannotti, M. Nanni, and D.
  Pedreschi. In Proc. SIAM Conference on Data
  Mining, pages 346357. SIAM, 2006.