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

Mete Celik, Shashi Shekhar, James P. Rogers, James A. Shine,

Jin Soung Yoo

Presented by: Mark Dietz, Jesse Vig

Background: Co-location Pattern Discovery

Extension of association rule mining to spatial domainTransaction replaced by neighborhoodFind object types that are associated by spatial

proximityFootball 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

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 = 1Participation ratio of CB in {WR, CB} = 2 / 2 = 1Participation index of {WR, CB} = min(1,1) = 1

MDCOP: Intuition

Adds element of time to co-location patternsSee football example belowParticipation 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

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?

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

Why is this important?

MilitaryIdentify patterns of attack

EcologyTracking predator-prey relationships

Homeland defenseSpotting suspicious behavior

Transportation Road and network planning

Why is this challenging?

Number of possible patterns grows exponentially with the number of different object types# of possible patterns = 2n, n = # of object

typesChallenge for pattern discovery in general

Interest measures are computationally expensive

Spatio-temporal datasets are huge

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.

Problem Solution: MDCOP Miner

Finds MDCOP's relatively efficientlyUses apriori algorithm

Builds larger candidate patterns from smaller ones: see figure below (important)

MDCOP measure is monotonically non-increasing

Extension of co-location miner

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 :

Contributions & Assumptions

ContributionsMDCOP framework

Independent of time order Operates on object types rather than objects

MDCOP Miner Validated analytically and experimentally

AssumptionsAbsolute number of co-occurrences

irrelevantRelative proportion of object types

irrelevant

Suggestions for Re-write

Introduce a spatial “support” measureReflects absolute number of co-occurrencesUsed as an additional filter, could aid

performance of MDCOP-MinerEvaluate performance against more data

sets, including very large ones.Are the MDCOPs found meaningful?

Questions?