1. Shashi ShekharMining For Spatial Patterns1 Mining for Spatial Patterns Shashi Shekhar Department of Computer Science University of Minnesota http://www.cs.umn.edu/~shekhar Collaborators: V. Kumar, G. Karypis, C.T. Lu, W. Wu, Y. Huang, V. Raju, P. Zhang, P. Tan, M. Steinbach This work was partially funded by NASA and Army High Performance Computing Center

2. Shashi ShekharMining For Spatial Patterns2 Spatial Data Mining(SDM) - Examples Historical Examples: London Asiatic Cholera 1854 (Griffith) Dental health and fluoride in water, Colorado early 1900s Current Examples: Cancer clusters (CDC), Spread of disease (e.g. Nile virus) Crime hotspots (NIJ CML, police petrol planning) Environmental justice (EPA), fair lending practices Upcoming Applications: Location aware services Defense: Sensor networks, Mobile ad-hoc networks Civilian: Mortgage PMI determination based on location

3. Shashi ShekharMining For Spatial Patterns3 Army Relevance of SDM Strategic Predicting global hot spots (FORMID) Army land: endangered species vs. training and war games Search for local trends in massive simulation data Critical infra-structure defense (threat assessment) Tactical Inferring enemy tactics (e.g. flank attack) from blobology Detection of lost ammunition dumps (Dr. Radhakrishnan) Operational Interpretation of maps: map matching (locating oneself on map) identify terrain feature, e.g. ravines, valleys, ridge, etc. Locating enemy (e.g. sniper in a haystack, sensor networks) Avoiding friendly fire

4. Shashi ShekharMining For Spatial Patterns4 Spatial Data Mining(SDM) - Definition Search of implicit, interesting patterns in geo-spatial data Ex. Reconnaissance, Vector maps(NIMA, TEC), GPS, Sensor networks Data Mining vs. Statistics: Primary vs. Secondary analysis Global vs. local trends Spatial Data Mining vs. Data Mining: Spatial Autocorrelation Continuous vs. Discrete data types

5. Shashi ShekharMining For Spatial Patterns5 Background Spatial Data Mining Spatial statistics in Geology, Regional Economics NSF workshop on GIS and DM (3/99) NSF workshop on spatial data analysis (5/02) Spatial patterns: Spatial outliers Location prediction Associations, colocations Hotspots, Clustering, trends, …

6. Shashi ShekharMining For Spatial Patterns6 Framework 2 Approaches to mining Spatial Data 1. Pick spatial features; use classical DM methods 2. Use novel data mining techniques Our Approach: Define the problem: capture special needs Explore data using maps, other visualization Try reusing classical DM methods If classical DM perform poorly, try new methods Evaluate chosen methods rigourously Performance tuning if needed

7. Shashi ShekharMining For Spatial Patterns7 Spatial Association Rule Citation: Symp. On Spatial Databases 2001 Problem: Given a set of boolean spatial features find subsets of co-located features, e.g. (fire, drought, vegetation) Data - continuous space, partition not natural, no reference feature Classical data mining approach: association rules But, Look Ma! No Transactions!!! No support measure! Approach: Work with continuous data without transactionizing it! confidence = Pr.[fire at s | drought in N(s) and vegetation in N(s)] support: cardinality of spatial join of instances of fire, drought, dry veg. participation: min. fraction of instances of a features in join result new algorithm using spatial joins and apriori_gen filters

8. Shashi ShekharMining For Spatial Patterns8 Event Definition Convert the time series into sequence of events at each spatial location.

9. Shashi ShekharMining For Spatial Patterns9 Interesting Association Patterns Use domain knowledge to eliminate uninteresting patterns. A pattern is less interesting if it occurs at random locations. Approach: Partition the land area into distinct groups (e.g., based on land- cover type). For each pattern, find the regions for which the pattern can be applied. If the pattern occurs mostly in a certain group of land areas, then it is potentially interesting. If the pattern occurs frequently in all groups of land areas, then it is less interesting.

10. Shashi ShekharMining For Spatial Patterns10 Association Rules Intra-zone non-sequential Patterns Shrubland regions FPAR-Hi  NPP-Hi (support  10) Region corresponds to semi-arid grasslands, a type of vegetation, which is able to quickly take advantage of high precipitation than forests. Hypothesis: FPAR-Hi events could be related to unusual precipitation conditions.

11. Shashi ShekharMining For Spatial Patterns11 Answers: and Can you find co-location patterns from the following sample dataset? Co-location

12. Shashi ShekharMining For Spatial Patterns12 Spatial Co-location A set of features frequently co-located Given A set T of K boolean spatial feature types T={f 1,f 2, …, f k } A set P of N locations P={p 1, …, p N } in a spatial frame work S, p i  P is of some spatial feature in T A neighbor relation R over locations in S Find T c =  subsets of T frequently co-located Objective Correctness Completeness Efficiency Constraints R is symmetric and reflexive Monotonic prevalence measure Reference Feature Centric Window CentricEvent Centric Co-location

13. Shashi ShekharMining For Spatial Patterns13 Participation index Participation ratio pr(f i, c) of feature f i in co-location c = {f 1, f 2, …, f k }: fraction of instances of f i with feature {f 1, …, f i-1, f i+1, …, f k } nearby 2.Participation index = min{pr(f i, c)} Algorithm Hybrid Co-location Miner Association rulesCo-location rules underlying spacediscrete setscontinuous space item-types events /Boolean spatial features collectionstransactionsneighborhoods prevalence measuresupportparticipation index conditional probability measure Pr.[ A in T | B in T ]Pr.[ A in N(L) | B at L ] Comparison with association rules Co-location

14. Shashi ShekharMining For Spatial Patterns14 Spatial Co-location Patterns Spatial feature A,B,C and their instances Possible associations are (A, B), (B, C), etc. Neighbor relationship includes following pairs: A1, B1 A2, B1 A2, B2 B1, C1 B2, C2 Dataset

15. Shashi ShekharMining For Spatial Patterns15 Spatial Co-location Patterns Spatial feature A,B, C, and their instances Support A,B =2 B,C=2 Support A,B=1 B,C=2 Partition approach [Yasuhiko, KDD 2001] Support not well defined,i.e. not independent of execution trace Has a fast heuristic which is hard to analyze for correctness/completeness Dataset

16. Shashi ShekharMining For Spatial Patterns16 Spatial Co-location Patterns Spatial feature A,B, C, and their instances Dataset Reference feature approach [Han SSD 95] C as reference feature to get transactions Transactions: (B1) (B2) Support (A,B) = Ǿ from Apriori algorithm Note: Neighbor relationship includes following pairs: A1, B1 A2, B1 A2, B2 B1, C1 B2, C2

17. Shashi ShekharMining For Spatial Patterns17 Spatial Co-location Patterns Spatial feature A,B, C, and their instances Our approach (Event Centric) Neighborhood instead of transactions Spatial join on neighbor relationship Support  Prevalence Participation index = min. p_ratio P_ratio(A, (A,B)) = fraction of instance of A participating in join(A,B, neighbor) Examples Support(A,B)=min(2/2,3/3)=1 Support(B,C)=min(2/2,2/2)=1 Dataset

18. Shashi ShekharMining For Spatial Patterns18 Spatial Co-location Patterns Spatial feature A,B, C, and their instances Support A,B =2 B,C=2 Support A,B=1 B,C=2 Support(A,B)=min(2/2,3/3)=1 Support(B,C)=min(2/2,2/2)=1 Partition approachOur approach Dataset Reference feature approach C as reference feature Transactions: (B1) (B2) Support (A,B) = Ǿ

19. Shashi ShekharMining For Spatial Patterns19 Spatial Outliers Spatial Outlier: A data point that is extreme relative to it neighbors Case Study: traffic stations different from neighbors [SIGKDD 2001, JIDA 2002] Data - space-time plot, distr. Of f(x), S(x) Distribution of base attribute: spatially smooth frequency distribution over value domain: normal Classical test - Pr.[item in population] is low Q? distribution of diff.[f(x), neighborhood agg{f(x)}] Insight: this statistic is distributed normally! Test: (z-score on the statistics) > 2 Performance - spatial join, clustering methods

20. Shashi ShekharMining For Spatial Patterns20 Spatial Outlier Detection Given A spatial graph G={V,E} A neighbor relationship (K neighbors) An attribute function : V -> R An aggregation function : :R k -> R A comparison function Confidence level threshold  Statistic test function ST: R ->{T, F} Find O = {v i | v i  V, v i is a spatial outlier} Objective Correctness: The attribute values of v i is extreme, compared with its neighbors Computational efficiency Constraints and ST are algebraic aggregate functions of and Computation cost dominated by I/O op.

21. Shashi ShekharMining For Spatial Patterns21 Spatial Outlier Detection Test 1. Choice of Spatial Statistic S(x) = [f(x)–E y  N(x) (f(y))] Theorem: S(x) is normally distributed if f(x) is normally distributed 2. Test for Outlier Detection | (S(x) -  s ) /  s | >  Hypothesis I/O cost determined by clustering efficiency f(x)S(x) Spatial Outlier Detection

22. Shashi ShekharMining For Spatial Patterns22 Original Data Variogram Cloud Moran Scatter Plot Graphical Spatial Tests

23. Shashi ShekharMining For Spatial Patterns23 A Unified Approach Spatial Outliers Original Data Our Approach Scatter Plot Tests : quantitative, graphical Results: Computation = spatial self-join Tests: algebraic functions of join Join predicate: neighbor relations I/O-cost: f(clustering efficiency) Our algorithm is I/O-efficient for Algebraic tests

24. Shashi ShekharMining For Spatial Patterns24 Results 1. CCAM achieves higher clustering efficiency (CE) 2. CCAM has lower I/O cost 3. High CE => low I/O cost 4. Big Page => high CE Z-order CCAM I/O costCE value Cell-Tree Spatial Outlier Detection

25. Shashi ShekharMining For Spatial Patterns25 Location Prediction Citations: IEEE Tran. on Multimedia 2002, SIAM DM Conf. 2001, SIGKDD DMKD 2000 Problem: predict nesting site in marshes given vegetation, water depth, distance to edge, etc. Data - maps of nests and attributes spatially clustered nests, spatially smooth attributes Classical method: logistic regression, decision trees, bayesian classifier but, independence assumption is violated ! Misses auto- correlation ! Spatial auto-regression (SAR), Markov random field bayesian classifier Open issues: spatial accuracy vs. classification accurary Open issue: performance - SAR learning is slow!

26. Shashi ShekharMining For Spatial Patterns26 Given: 1. Spatial Framework 2. Explanatory functions: 3. A dependent class: 4. A family of function mappings: Find: Classification model: Objective:maximize classification_accuracy Constraints: Spatial Autocorrelation exists Nest locations Distance to open water Vegetation durability Water depth Location Prediction

27. Shashi ShekharMining For Spatial Patterns27 Motivation and Framework

28. Shashi ShekharMining For Spatial Patterns28 Spatial Autoregression Model (SAR) y =  Wy + X  +  W models neighborhood relationships  models strength of spatial dependencies  error vector Solutions  and  - can be estimated using ML or Bayesian stat. e.g., spatial econometrics package uses Bayesian approach using sampling-based Markov Chain Monte Carlo (MCMC) method. Likelihood-based estimation requires O(n 3 ) ops. Other alternatives – divide and conquer, sparse matrix, LU decomposition, etc. Spatial AutoRegression (SAR)

29. Shashi ShekharMining For Spatial Patterns29 Evaluation Linear Regression Spatial Regression Spatial model is better

30. Shashi ShekharMining For Spatial Patterns30 Markov Random Field based Bayesian Classifiers Pr(l i | X, L i ) = Pr(X|l i, L i ) Pr(l i | L i ) / Pr (X) Pr(l i | L i ) can be estimated from training data L i denotes set of labels in the neighborhood of si excluding labels at si Pr(X|l i, L i ) can be estimated using kernel functions Solutions stochastic relaxation [Geman] Iterated conditional modes [Besag] Graph cut [Boykov] MRF Bayesian

31. Shashi ShekharMining For Spatial Patterns31 Experiment Design

32. Shashi ShekharMining For Spatial Patterns32 Prediction Maps(Learning) MRF-P Prediction (ADNP=3.36) Actual Nest Sites (Real Learning) MRF-GMM Prediction (ADNP=5.88)SAR Prediction (ADNP=9.80) NZ=85NZ=138 NZ=140NZ=130

33. Shashi ShekharMining For Spatial Patterns33 Prediction Maps(Testing) Actual Nest Sites (Real Learning) MRF-P Prediction (ADNP=2.84) Actual Nest Sites (Real Testing) SAR Prediction (ADNP=8.63) MRF-GMM Prediction (ADNP=3.35) NZ=30 NZ=80 NZ=76 NZ=80

34. Shashi ShekharMining For Spatial Patterns34 SAR can be rewritten as y = (QX)  + Q  where Q = (I-  W) -1 which can be viewed as a spatial smoothing operation. This transformation shows that SAR is similar to linear logistic model, and thus suffers with same limitations – i.e., SAR model assumes linear separability of classes in transformed feature space SAR model also make more restrictive assumptions about the distribution of features and class shapes than MRF The relationship between SAR and MRF are analogous to the relationship between logistic regression and Bayesian classifiers. Our experimental results shows that MRF model yields better spatial and classification accuracies than SAR predictions. Comparison (MRF-BC vs. SAR)

35. Shashi ShekharMining For Spatial Patterns35 Confusion Matrix: Spatial Confusion Matrix: MRF vs. SAR

36. Shashi ShekharMining For Spatial Patterns36 Conclusion and Future Directions Spatial domains may not satisfy assumptions of classical methods data: auto-correlation, continuous geographic space patterns: global vs. local, e.g. spatial outliers vs. outliers data exploration: maps and albums Open Issues patterns: hot-spots, blobology (shape), spatial trends, … metrics: spatial accuracy(predicted locations), spatial contiguity(clusters) spatio-temporal dataset scale and resolutions sentivity of patterns geo-statistical confidence measure for mined patterns

37. 37 Army Relevance and Collaborations Relevance: “Maps are as important to soldiers as guns” - unknown Joint Projects: High Performance GIS for Battlefield Simulation (ARL Adelphi) Spatial Querying for Battlefield Situation Assessment (ARL Adelphi) Joint Publications: w/ G. Turner (ARL Adelphi, MD) & D. Chubb (CECOM IEWD) IEEE Computer (December 1996) IEEE Transactions on Knowledge and Data Eng. (July-Aug. 1998) Three conference papers Visits, Other Collaborations GIS group, Waterways Experimentation Station (Army) Concept Analysis Agency, Topographic Eng. Center, ARL, Adelphi Workshop on Battlefield Visualization and Real Time GIS (4/2000)

38. Shashi ShekharMining For Spatial Patterns38 Reference 1.S. Shekhar, S. Chawla, S. Ravada, A. Fetterer, X. Liu and C.T. Liu, “Spatial Databases: Accomplishments and Research Needs”, IEEE Transactions on Knowledge and Data Engineering, Jan.-Feb. 1999. 2.S. Shekhar and Y. Huang, “Discovering Spatial Co-location Patterns: a Summary of Results”, In Proc. of 7th International Symposium on Spatial and Temporal Databases (SSTD01), July 2001. 3.S. Shekhar, C.T. Lu, P. Zhang, "Detecting Graph-based Spatial Outliers: Algorithms and Applications“, the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2001. 4.S. Shekhar, C.T. Lu, P. Zhang, “Detecting Graph-based Saptial Outlier”, Intelligent Data Analysis, To appear in Vol. 6(3), 2002 5.S. Shekhar, S. Chawla, the book “Spatial Database: Concepts, Implementation and Trends”, Prentice Hall, 2002 6.S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Extending Data Mining for Spatial Applications: A Case Study in Predicting Nest Locations”, Proc. Int. Confi. on 2000 ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD 2000), Dallas, TX, May 14, 2000. 7.S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Modeling Spatial Dependencies for Mining Geospatial Data”, First SIAM International Conference on Data Mining, 2001. 8.S. Shekhar, P.R. Schrater, R. R. Vatsavai, W. Wu, and S. Chawla, “Spatial Contextual Classification and Prediction Models for Mining Geospatial Data”,To Appear in IEEE Transactions on Multimedia, 2002. 9.S. Shekhar, V. Kumar, P. Tan. M. Steinbach, Y. Huang, P. Zhang, C. Potter, S. Klooster, “Mining Patterns in Earth Science Data”, IEEE Computing in Science and Engineering (Submitted)

39. Shashi ShekharMining For Spatial Patterns39 Reference 10.S. Shekhar, C.T. Lu, P. Zhang, “A Unified Approach to Spatial Outliers Detection”, IEEE Transactions on Knowledge and Data Engineering (Submitted) 11.S. Shekhar, C.T. Lu, X. Tan, S. Chawla, Map Cube: A Visualization Tool for Spatial Data Warehouses, as Chapter of Geographic Data Mining and Knowledge Discovery. Harvey J. Miller and Jiawei Han (eds.), Taylor and Francis, 2001, ISBN 0-415-23369-0. 12.S. Shekhar, Y. Huang, W. Wu, C.T. Lu, What's Spatial about Spatial Data Mining: Three Case Studies, as Chapter of Book: Data Mining for Scientific and Engineering Applications. V. Kumar, R. Grossman, C. Kamath, R. Namburu (eds.), Kluwer Academic Pub., 2001, ISBN 1-4020-0033-2 13.Shashi Shekhar and Yan Huang, Multi-resolution Co-location Miner: a New Algorithm to Find Co-location Patterns in Spatial Datasets, Fifth Workshop on Mining Scientific Datasets (SIAM 2nd Data Mining Conference), April 2002