Cascading Spatio-Temporal Pattern Discovery

1. CSci 8715 Cascading Spatio-Temporal Pattern Discovery P. Mohan, S.Shekhar, J. Shine, J. Rogers Presented by: Atanu Roy Akash Agrawal

2. CSci 8715 Motivation • Applications in domains like • Public safety • Climate modeling • Natural disaster planning

3. CSci 8715 The Problem • Input • ST dataset consisting of a set of booleanevent-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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5. CSci 8715 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

6. Related Works Spatio-temporal frequent patterns Others Partially Ordered 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”. 6

7. CSci 8715 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

8. CSci 8715 Key Concepts

9. CSci 8715 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 * The paper should have addressed the issue that the filters are complimentary in nature and should be used together to achieve the desired results.

10. CSci 8715 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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12. CSci 8715 Validations • Mathematical proofs & Statistical Interpretation • Diggleet al.’s K-function • Determination of the impact of filtering • Comparison of performance of the 2 different CSTPM algorithms

13. CSci 8715 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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15. CSci 8715 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.

16. CSci 8715 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.

17. CSci 8715 Thank You • 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. • 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. • 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. • M. Celik, S. Shekhar, B. George, J.P. Rogers, and J.A. Shine, “Discovering and quantifying mean streets: A summary of results”, (2007).