Cascading Spatio-Temporal Pattern Discovery

P. Mohan, S.Shekhar, J. Shine, J. Rogers

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Presented by: Atanu RoyAkash Agrawal

Motivation

• Applications in domains like

– Public safety

– Climate modeling

– Natural disaster planning

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The Problem

• Input– ST dataset consisting of a set of boolean event-types

over a common ST framework– a directed neighborhood relation– a threshold CPI

• Output– CSTPS with CPI ≥ threshold

• Objective– Minimize Computation cost

• Constraints– Correctness, completeness

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Key Challenges• Absence of natural

transactions & overlap across instances

• Exponential cardinality of candidate patterns

• Computationally complex ST neighborhood

• Conflicting demands of computational scalability and statistical interpretation

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6

Related WorksSpatio-temporal frequent patterns

Partially OrderedOthers

Unordered(ST Co-occurrence)

Totally Ordered(ST Sequences)

This 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 Does not capture partially ordered relationships 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.

Slide Courtesy: Pradeep Mohan. Used in the class for demonstrating “Articulating Novelty”.

Novel & Better!

• Novelty– Implementation of partial ordered ST framework.– Spatio-temporal statistical interpretation first introduced – Novel interest measure– 2 filtering strategies– New measure (clumpiness degree) – Tested on novel datasets

• Better– Bottleneck analysis shows major time is utilized for interest

measure evaluation– Computes interest measure using ST partitioning– Algebraic cost model for filtering– Comparison shows better performance from authors’ previous work

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Key Concepts

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Filters• Upper Bound (UB) Filter*:

– Has anti-monotone upper bound.– Reflects maximum possible values of interest

measure.

• Multi-resolution Spatio-Temporal Filter: *– There exists a low dimensional embedding in space

and time– Used to create a coarse CPI which is later proved to

never underestimate the CPI– Can be used for pruning patterns with low CPI– Saves time since actual CPI computation is very

expensive

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* The paper should have addressed the issue that the filters are complimentary in nature and should be used together to achieve the desired results.

Description

• Description: for each size k pattern– Apply UB filter

– for k in (1,2,…n) do • Generate size k candidates using CSTPs of size (k-

1) recursively

• Perform MST filtering for non-prevalent patterns

• Generate pattern instance and compute CPI

• Prune non-prevalent and generate prevalent CSTP

– end for

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Validations

• Mathematical proofs & Statistical Interpretation– Diggle et al.’s K-function

• Determination of the impact of filtering

• Comparison of performance of the 2 different CSTPM algorithms

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Assumptions• Use of Euclidean distance for the distance

instead of real network distance.• Helpful only -when the network is very well-

connected.• In real world, Euclidean distance is rarely the “true”

distance between two points. • Fails to capture dynamic constraints.

– Police patrol can not cross a river unless there is a bridge.

– Washington Ave. is closed for vehicular movements for the next few years.

• Most intuitive is the use of underlying spatial network distance instead.

– esp. Road Network– River Network

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Assumptions

• ST events are boolean.– Domains like climate study has attributes

which can have REAL data.

• ST non-stationarities, choices of directed neighborhood relations are beyond the scope.– Events like drunk driving can be considered as

non-stationary and will change with respect to time.

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Critique

• The approach used for candidate generation can be improved further to reduce the computational complexity.– Implementation of hash indices for checking

sub-graph isomorphism can be tried.

• Joins can also be used for shortest path computation.

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Thank You1. P. Mohan, S. Shekhar, J. A. Shine

and J. P. Rogers, "Cascading spatio-temporal pattern dis-covery: A summary of results," in SDM, 2010, pp. 327 - 338.

2. J. A. Shine, J. P. Rogers, S. Shekhar and P. Mohan, "Discovering partially ordered patterns of Terrorism via Spatio-temporal Data Mining," in 16th Army conference on Applied Statistics, Cory, NC, USA, 2010.

3. J. A. Shine, J. P. Rogers, S. Shekhar and P. Mohan, "Cascade models for spatio-temporal pattern discovery," in 1st USACE Research and Development Conference, Memphis, TN , USA, 2009.

4. M. Celik, S. Shekhar, B. George, J.P. Rogers, and J.A. Shine, “Discovering and quantifying mean streets: A summary of results”, (2007).

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