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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 Shashi Shekhar Mining For Spatial Patterns 1 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 Shashi Shekhar Mining For Spatial Patterns 2 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 Shashi Shekhar Mining For Spatial Patterns 3 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 Shashi Shekhar Mining For Spatial Patterns 4 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, … Shashi Shekhar Mining For Spatial Patterns 5 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 Shashi Shekhar Mining For Spatial Patterns 6 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 Shashi Shekhar Mining For Spatial Patterns 7 Event Definition Convert the time series into sequence of events at each spatial location. time y t1 AK M A B AB D DF CM ABE G AB G DL J x AB D AB DEF EG K BCD CE F EG M BCE Shashi Shekhar t3 t2 DK L AB GL CFM AB E Grid Cell (x,y) (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4) Mining For Spatial Patterns t1 Æ {A, B, D} Æ {A, K, M} {B, C, E} Æ Æ {A, B} Æ {A, B, G} {C, M} Æ Æ Æ Æ Æ t2 Æ {D, L, J} {A, B, E, G} Æ {E, G, M} {C, E, F} Æ {D, F} Æ Æ Æ Æ Æ {D, K, L} Æ {A, B} t3 Æ Æ {B, C, D} Æ {C, F, M} {A, B, G, L} Æ {A, B, D} Æ {A, B, E} Æ Æ Æ Æ {E, G, K} {D, E, F} 8 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 landcover 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. Shashi Shekhar Mining For Spatial Patterns 9 Association Rules Intra-zone non-sequential Patterns FPAR-Hi NPP-Hi (support 10) Shrubland regions • 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. Shashi Shekhar Mining For Spatial Patterns 10 Co-location Can you find co-location patterns from the following sample dataset? Answers: Shashi Shekhar and Mining For Spatial Patterns 11 Co-location Spatial Co-location A set of features frequently co-located Given A set T of K boolean spatial feature types T={f1,f2, … , fk} A set P of N locations P={p1, …, pN } in a spatial frame work S, pi P is of some spatial feature in T A neighbor relation R over locations in S Find Reference Feature Centric Tc = subsets of T frequently co-located Objective Correctness Completeness Efficiency Constraints R is symmetric and reflexive Monotonic prevalence measure Window Centric Shashi Shekhar Mining For Spatial Patterns Event Centric 12 Co-location Comparison with association rules Association rules Co-location rules underlying space discrete sets continuous space item-types item-types events /Boolean spatial features collections transactions neighborhoods prevalence measure support participation index conditional probability measure Pr.[ A in T | B in T ] Pr.[ A in N(L) | B at L ] Participation index Participation ratio pr(fi, c) of feature fi in co-location c = {f1, f2, …, fk}: fraction of instances of fi with feature {f1, …, fi-1, fi+1, …, fk} nearby 2.Participation index = min{pr(fi, c)} Algorithm Hybrid Co-location Miner Shashi Shekhar Mining For Spatial Patterns 13 Spatial Co-location Patterns Dataset • 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 Shashi Shekhar Mining For Spatial Patterns 14 Spatial Co-location Patterns Dataset 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 Spatial feature A,B, C, and their instances Support A,B =2 B,C=2 Shashi Shekhar Mining For Spatial Patterns Support A,B=1 B,C=2 15 Spatial Co-location Patterns Dataset Reference feature approach [Han SSD 95] •C as reference feature to get transactions •Transactions: (B1) (B2) •Support (A,B) = Ǿ from Apriori algorithm Spatial feature A,B, C, and their instances Shashi Shekhar •Note: Neighbor relationship includes following pairs: •A1, B1 •A2, B1 •A2, B2 •B1, C1 •B2, C2 Mining For Spatial Patterns 16 Spatial Co-location Patterns Dataset 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 Shashi Shekhar Mining For Spatial Patterns 17 Spatial Co-location Patterns Dataset Partition approach Our approach Support(A,B)=min(2/2,3/3)=1 Support(B,C)=min(2/2,2/2)=1 Spatial feature A,B, C, and their instances Support A,B =2 B,C=2 Reference feature approach C as reference feature Transactions: (B1) (B2) Support (A,B) = Ǿ Support A,B=1 B,C=2 Shashi Shekhar Mining For Spatial Patterns 18 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 Shashi Shekhar Mining For Spatial Patterns 19 Spatial Outlier Detection Given A spatial graph G={V,E} A neighbor relationship (K neighbors) An attribute function f : V -> R An aggregation function : Faggr :R k -> R A comparison function Fdiff ( f , Faggr ) Confidence level threshold Statistic test function ST: R ->{T, F} Find O = {vi | vi V, vi is a spatial outlier} Objective Correctness: The attribute values of vi is extreme, compared with its neighbors Computational efficiency Constraints Fdiff and ST are algebraic aggregate functions of f and Faggr Computation cost dominated by I/O op. Shashi Shekhar Mining For Spatial Patterns 20 Spatial Outlier Detection 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) Shashi Shekhar Mining For Spatial Patterns S(x) 21 Graphical Spatial Tests Moran Scatter Plot Original Data Variogram Cloud Shashi Shekhar Mining For Spatial Patterns 22 A Unified Approach Spatial Outliers •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 Scatter Plot Original Data Our Approach Shashi Shekhar Mining For Spatial Patterns 23 Spatial Outlier Detection 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 CE value Cell-Tree Shashi Shekhar CCAM Mining For Spatial Patterns I/O cost Z-order 24 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 autocorrelation ! Spatial auto-regression (SAR), Markov random field bayesian classifier Open issues: spatial accuracy vs. classification accurary Open issue: performance - SAR learning is slow! Shashi Shekhar Mining For Spatial Patterns 25 Location Prediction Given: 1. Spatial Framework S {s1 ,...sn } 2. Explanatory functions: f X : S R 3. A dependent class: fC : S C {c1 ,...cM } 4. A family of function mappings: R ... R C k Find: Classification model: fˆc Nest locations Distance to open water Objective:maximize ˆ classification_accuracy ( f c , f c ) Constraints: Spatial Autocorrelation exists Vegetation durability Shashi Shekhar Mining For Spatial Patterns Water depth 26 Motivation and Framework Shashi Shekhar Mining For Spatial Patterns 27 Spatial AutoRegression (SAR) • 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(n3) ops. • Other alternatives – divide and conquer, sparse matrix, LU decomposition, etc. Shashi Shekhar Mining For Spatial Patterns 28 Evaluation Linear Regression y X Spatial Regression y Wy X Spatial model is better Shashi Shekhar Mining For Spatial Patterns 29 MRF Bayesian • Markov Random Field based Bayesian Classifiers • Pr(li | X, Li) = Pr(X|li, Li) Pr(li | Li) / Pr (X) • Pr(li | Li) can be estimated from training data • Li denotes set of labels in the neighborhood of si excluding labels at si • Pr(X|li, Li) can be estimated using kernel functions • Solutions • stochastic relaxation [Geman] • Iterated conditional modes [Besag] • Graph cut [Boykov] Shashi Shekhar Mining For Spatial Patterns 30 Experiment Design Shashi Shekhar Mining For Spatial Patterns 31 Prediction Maps(Learning) Actual Nest Sites (Real Learning) MRF-P Prediction (ADNP=3.36) NZ=85 NZ=138 MRF-GMM Prediction (ADNP=5.88) SAR Prediction (ADNP=9.80) NZ=140 Shashi Shekhar NZ=130 Mining For Spatial Patterns 32 Prediction Maps(Testing) Actual Nest Sites (Real Testing) MRF-P Prediction (ADNP=2.84) Actual Nest Sites (Real Learning) NZ=30 NZ=80 MRF-GMM Prediction (ADNP=3.35) NZ=76 Shashi Shekhar SAR Prediction (ADNP=8.63) NZ=80 Mining For Spatial Patterns 33 Comparison (MRF-BC vs. SAR) • • • • 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. Shashi Shekhar Mining For Spatial Patterns 34 MRF vs. SAR Confusion Matrix: Spatial Confusion Matrix: Shashi Shekhar Mining For Spatial Patterns 35 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 Shashi Shekhar Mining For Spatial Patterns 36 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) 37 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) Shashi Shekhar Mining For Spatial Patterns 38 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 Shashi Shekhar Mining For Spatial Patterns 39