Spatio-temporal frequent pattern mining for public safety: Concepts and Techniques Pradeep Mohan * Department of Computer Science University of Minnesota, Twin-Cities Advisor: Prof. Shashi Shekhar Thesis Committee: Prof. F. Harvey, Prof. G. Karypis, Prof. J. Srivastava *Contact: [email protected]
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Spatio-temporal frequent pattern mining for public safety: Concepts and Techniques
Spatio-temporal frequent pattern mining for public safety: Concepts and Techniques. Pradeep Mohan * Department of Computer Science University of Minnesota, Twin-Cities Advisor: Prof. Shashi Shekhar Thesis Committee: Prof. F. Harvey, Prof. G. Karypis, Prof. J. Srivastava. - PowerPoint PPT Presentation
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Spatio-temporal frequent pattern mining for public safety: Concepts and Techniques
Pradeep Mohan*
Department of Computer ScienceUniversity of Minnesota, Twin-Cities
Advisor: Prof. Shashi ShekharThesis Committee: Prof. F. Harvey, Prof. G. Karypis, Prof. J. Srivastava
P.Mohan, S.Shekhar, J.A. Shine, J.P. Rogers, Z.Jiang, N.Wayant. A spatial neighborhood graph based approach to Regional co-location pattern discovery: summary of results. In Proc. Of 19th ACM SIGSPATIAL International Conference on Advances in GIS 2011 (ACM SIGSPATIAL 2011, Full paper acceptance rate 23%)
Crime Pattern Analysis Application (Chapter 4)
S.Shekhar, P. Mohan, D.Oliver, Z.Jiang, X.Zhou. Crime pattern analysis: A spatial frequent pattern mining approach. M. Leitner (Ed.), Crime modeling and mapping using Geospatial Technologies, Springer (Accepted with Revisions).
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Outline
IntroductionMotivation
Problem Statement
Future Work
Our Approach
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Motivation: Public Safety
Identifying events (e.g. Bar closing, football games) that lead to increased crime.
Crime generators and attractors
Identifying frequent crime hotspots
Law enforcement planning
Predicting crime events
Predictive policing (e.g. Predict next location of offense, forecast crime levels around conventions etc.)
Predicting the next location of burglary.Courtsey: www.startribune.com
Question: What / Where are the frequent crime generators ?
Question: Where are the crime hotspots ?
Question: What are the crime levels 1 hour after a football game within a radius of 1 mile ?
Crime Event: Motivated offender, vulnerable victim (available at an appropriate location and time), absence of a capable guardian.
Crime Generators : offenders and targets come together in time place, large gatherings (e.g. Bars, Football games) Crime Attractors : places offering many criminal opportunities and offenders may relocate to these areas (e.g. drug areas)
Problem Statement Spatio-temporal frequent pattern mining problem Challenges
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Spatio-temporal frequent pattern mining problem
Given : Spatial / Spatio-temporal framework. Crime Reports with type, location and / or time. Spatial Features of interest (e.g. Bars). Interest measure threshold (Pθ) Spatial / Spatio-temporal neighbor relation.
Find: Frequent patterns with interestingness >= Pθ
Objective : Minimize computation costs.
Constraints : Correctness and Completeness. Statistical Interpretation (i.e. account for autocorrelation or
Computational Cost Exponential set of Candidate patterns
Time T1 Time T3>T2Time T2 > T1
B.2
B.1 C.2C.3C.1
C.4
A.1
A.3
A.2A.4
A.5
a
Aggregate(T1,T2,T3)
B.1
B.2
A.2A.4
C.2
C.3
C.4
A.5
C.1
A.1
A.3
Time partitioning misses relationships
Space partitioning misses relationships
{Null}
A B A C B A B C C A C B
C
B A
B
C A
C
B A
A
B C
C
A B……….……….
C
A B
B
A C
A
B C
C
B A
B
C A
A
C B
# Patterns = Exponential (# event types)
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Our Contributions
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New Spatio-temporal frequent pattern families. Ex: Cascading ST Patterns and Regional Co-location patterns.
Novel interest measures guarantee statistical interpretation and computable in polynomial time.
Scalable algorithms based on properties of spatio-temporal data and interest measures.
Experimental evaluation using synthetic and real crime datasets.
Outline
Introduction
Future Work
Problem Statement
Our Approach Big Picture Cascading Spatio-temporal pattern discovery Other Frequent Pattern Families
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Cascading ST pattern (CSTP)
Output: CSTP
Partially ordered subsets of ST event types.
Located together in space.
Occur in stages over time.
B A
C
CSTP: P1
Aggregate(T1,T2,T3)
Time T1
Assault(A) Drunk Driving (C)
Bar Closing(B)
Time T3>T2Time T2 > T1
a
Input: Crime reports with location and time.
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Related Pattern Semantics: ST Data mining
Spatio-temporal frequent patterns
Partially OrderedOthers
Unordered(ST Co-occurrence)
Totally Ordered(ST Sequences)
Our Work(Cascading ST patterns )
ST Co-occurrence [Celik et al. 2008, Cao et al. 2006] Designed for moving object datasets by treating trajectories as location time series Performs partitioning over space and time.
ST Sequence [Huang et al. 2008, Cao et al. 2005 ]Totally ordered patterns modeled as a chain. Does not account for multiply connected patterns(e.g. nonlinear) Misses non-linear semantics. No ST statistical interpretation.
Subsets of spatial features. Frequently located in certain regions of a study area.
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Statistical Foundation: Accounting for Heterogenity
Regional Participation Ratio
Regional Participation index
Example
€
;RPR(< {ABC},PL2 >,B) =2
6
€
RPR(< {ABC},PL2 >,C) =1
4
€
RPI(< {ABC},PL2 >) = min2
4,2
6,1
4
⎧ ⎨ ⎩
⎫ ⎬ ⎭=
1
4
Conditional probability of observing a pattern instance within a locality given an instance of a feature within that locality.
Example
Quantifies the local fraction participating in a relationship.
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Conclusions
Proposed SFPM techniques (e.g., Cascading ST Patterns and Regional Co-location patterns) honor ST Semantics (e.g., Partial order, Continuity).
Interest measures achieve a balance between statistical interpretation and computational scalability.
Algorithmic strategies exploiting properties of ST data (e.g., multiresolution filter) and properties of interest measures enhance computational savings.
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Future Work – Short and Medium Term
Input Data
Spatial Spatio-temporal (ST)
Pattern Semantics Unordered ✔ ✔
Totally Ordered X ✔
Partially Ordered X CSTP discovery
Statistical Foundation
Autocorrelation ✔ CSTP discovery
Heterogeneity RCP Discovery X
Underlying Framework
Euclidean RCP Discovery CSTP discovery
Non-Euclidean (Networks) X X
Neighbor Relation User specified RCP Discovery CSTP discovery
Type of data Boolean / Categorical RCP Discovery CSTP discovery
Quantitative data (e.g., Climate) X X
X: Unexplored
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Future Work – Long Term
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Exploring interpretation of discovered patterns by law enforcement.
ST Predictive analytics, Predictive models based on SFPM and Predictive policing.
Towards Geo-social analytics for policing (e.g. Criminal Flash mobs, gangs, groups of offenders committing crimes)
New ST frequent pattern mining algorithms based on depth first graph enumeration.
ST frequent pattern mining techniques that account for patron demographic levels.
Explore evaluation of choloropeth maps via ST frequent pattern mining.
Acknowledgment
Members of the Spatial Database and Data Mining Research Group University of Minnesota, Twin-Cities.
This Work was supported by Grants from U.S.ARMY, NGA and U.S. DOJ.
Advisor: Prof. Shashi Shekhar, Computer Science, University of Minnesota.
Thesis committee.
U.S. DOJ – National Institute of Justice: Mr. Ronald E. Wilson (Program Manager, Mapping and Analysis for Public Safety) , Dr. Ned Levine (Ned Levine and Associates, CrimeStat Program)
U.S. Army – Topographic Engineering Center: Dr. J.A.Shine (Mathematician and Statistician, Geospatial Research and Engineering Division ) and Dr. J.P. Rogers (Additional Director, Topographic Engineering Center)
Mr. Tom Casady, Public Safety Director (Formerly Lincoln Police Chief), Lincoln, NE, USA
Thank You for your Questions, Comments and Attention!