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

Motivation Applications in domains like –Public safety –Climate modeling –Natural disaster planning CSci 8715

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 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 CSci 8715

6 Related Works Spatio-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 ]  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 CSci 8715

Key Concepts 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 CSci 8715 * 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 CSci 8715

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 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 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. 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. CSci 8715

Thank You 1.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 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, 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, M. Celik, S. Shekhar, B. George, J.P. Rogers, and J.A. Shine, “Discovering and quantifying mean streets: A summary of results”, (2007). CSci 8715