Mixed-Drove Spatio-Temporal Co-occurrence Pattern Mining: A Summary of Results

1. Mete Celik, Shashi Shekhar, James P. Rogers, James A. Shine, Jin Soung Yoo Presented by: Mark Dietz, Jesse Vig Mixed-Drove Spatio-Temporal Co-occurrence Pattern Mining: A Summary of Results

2. Background: Co-location Pattern Discovery • Extension of association rule mining to spatial domain • Transaction replaced by neighborhood • Find object types that are associated by spatial proximity • Football example: • 3 object types: Wide receiver (WR), Cornerback (CB), and Quarterback (Q) • Particular instances of each type are indexed numerically, e.g. WR.1, WR.2 • {WR, CB} forms a co-location pattern

3. Background: Participation Index • Measures “prevalence” of a co-location pattern • Given a subset P of object types, • Participation ratio for each object type in P is the proportion of instances of that type that are co-located with instances of the other object types in P • Participation index is the minimum participation ratio of all object types in P • A co-location pattern is prevalent if the participation index of that pattern is above a threshold θp Participation ratio of WR in {WR, CB} = 2 / 2 = 1 Participation ratio of CB in {WR, CB} = 2 / 2 = 1 Participation index of {WR, CB} = min(1,1) = 1

4. MDCOP: Intuition • Adds element of time to co-location patterns • See football example below • Participation index only works for individual time slots • Participation index of {WR, CB} is 1 for t=0,2 but 0 for t=1,3 • MDCOP: co-location patterns that persist over time • MDCOP: Mixed-drove spatio-temporal co-occurrence patterns

5. MDCOP: Formal definitions • Time prevalence: • Fraction of time slots in which a given pattern occurs. • Mixed-drove prevalence: • Composition of spatial prevalence (participation index) and time prevalence. • Assume a spatial prevalence threshold θp • Mixed-drove prevalence is the fraction of time slots with participation index ≥ θp • Example (below): If θp= .5, what is the mixed-drove prevalence of {WR, CB}? • Given a time prevalence threshold θtime ,an MDCOP is a mixed-drove prevalent pattern if mixed-drove prevalence ≥ θtime • Example: If If θp= .5 and θtime=.7, is the {WR, CB} mixed-drove prevalent?

6. Problem Statement • Given: • A set P of Boolean spatio-temporal object-types • A neighbor relation R over locations • A spatial prevalence threshold θp • A time prevalence threshold θtime • Find: • {Pi | Pi is a subset of P and Pi is prevalent MDCOP} • Objective: • Minimize computation cost • Constraints: • Solution set must be correct • i.e. all identified patterns are prevalent MDCOPs • Solution set must be complete • i.e. finds all prevalent MDCOPs

7. Why is this important? Military • Identify patterns of attack Ecology • Tracking predator-prey relationships Homeland defense • Spotting suspicious behavior Transportation • Road and network planning

8. Why is this challenging? • Number of possible patterns grows exponentially with the number of different object types • # of possible patterns = 2n, n = # of object types • Challenge for pattern discovery in general • Interest measures are computationally expensive • Spatio-temporal datasets are huge

9. Limitations of Related Work • Mining uniform groups of moving objects, i.e. flock patterns • Doesn't apply to mixed object types • Mining mixed groups of moving objects, i.e. mixed droves • Only looks for patterns in consecutive time slots • Only looks for patterns between specific objects rather than object-types.

10. Problem Solution: MDCOP Miner • Finds MDCOP's relatively efficiently • Uses apriori algorithm • Builds larger candidate patterns from smaller ones: • see figure below (important) • MDCOP measure is monotonically non-increasing • Extension of co-location miner

11. Validation • Analytical results • Mixed-drove prevalence measure is monotonically non-increasing • MDCOP Miner is correct and complete • Total cost of MDCOP Miner is no worse than naïve approach. • Experimental results • Compared run-time of MDCOP Miner to naive approach • Sample results :

12. Contributions & Assumptions • Contributions • MDCOP framework • Independent of time order • Operates on object types rather than objects • MDCOP Miner • Validated analytically and experimentally • Assumptions • Absolute number of co-occurrences irrelevant • Relative proportion of object types irrelevant

13. Suggestions for Re-write • Introduce a spatial “support” measure • Reflects absolute number of co-occurrences • Used as an additional filter, could aid performance of MDCOP-Miner • Evaluate performance against more data sets, including very large ones. • Are the MDCOPs found meaningful?

14. Questions?