Mining for Spatial Patterns

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

2. Background • NSF workshop on GIS and DM (3/99) • Spatial data - traffic, bird habitats, global climate, logistics, ... • For spatial patterns - outliers, location prediction, associations, sequential associations, clustering, trends, … Mining For Spatial Patterns

3. Framework • Problem statement: capture special needs • Data exploration: maps, new methods • Try reusing classical methods • from data mining, spatial statistics • If reuse is not possible, invent new methods • Validation, Performance tuning Mining For Spatial Patterns

4. Research Goals • Research Goals: • modeling of ecological data • event modeling • zone modeling. • finding spatio-temporal patterns • associations • predictive models. A key interest is finding connections between the ocean and the land. Mining For Spatial Patterns

5. Sources of Earth Science Data • Before 1950, very sparse, unreliable data. • Since 1950, reliable global data. • Ocean temperature and pressure are based on data from ships. • Most land data, (solar, precipitation, temperature and pressure) comes from weather stations. • Since 1981, data has been available from Earth orbiting satellites. • FPAR, a measure related to plant • Since 1999 TERRA, the flagship of the NASA Earth Observing System, is providing much more detailed data. Mining For Spatial Patterns

6. Example Pattern: Teleconnections • Teleconnections are the simultaneous variation in climate and related processes over widely separated points on the Earth. • For example, El Nino is the anomalous warming of the eastern tropical region of the Pacific, and has been linked to various climate phenomena. • Droughts in Australia and Southern Africa • Heavy rainfall along the western coast of South America • Milder winters in the Midwest Mining For Spatial Patterns

7. Net Primary Production (NPP) • Net Primary Production (NPP) is the net assimilation of atmospheric carbon dioxide (CO2) into organic matter by plants. • NPP is driven by solar radiation and can be constrained by precipitation and temperature. • NPP is a key variable for understanding the global carbon cycle and ecological dynamics of the Earth. • Keeping track of NPP is important because it includes the food source of humans and all other organisms. • Sudden changes in the NPP of a region can have a direct impact on the regional ecology. • An ecosystem model for predicting NPP, CASA (the Carnegie Ames Stanford Approach) provides a detailed view of terrestrial productivity. Mining For Spatial Patterns

8. Benefits of Data Mining • Data mining provides earth scientist with tools that allow them to spend more time choosing and exploring interesting families of hypotheses. • However, statistics is needed to provide methods for determining the “statistical” significance of results. • By applying the proposed data mining techniques, some of the steps of hypothesis generation and evaluation will be automated, facilitated and improved. • Association rules provide a “new” framework for detecting relationships between events. Mining For Spatial Patterns

9. Approaches Mining For Spatial Patterns

10. Clustering • Interested in relationships between regions, not “points.” • For land, clustering based on NPP or other variables, e.g., precipitation, temperature. • For ocean, clustering based on SST (Sea Surface Temperature). • When “raw” NPP and SST are used, clustering can find seasonal patterns. • Anomalous regions have plant growth patterns which reversed from those typically observed in the hemisphere in which they reside, and are easy to spot. Mining For Spatial Patterns

11. Clustering El Nino Regions SNN clusters of SST that are highly correlated with El Nino indices. Mining For Spatial Patterns

12. 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 Mining For Spatial Patterns

13. Event Definition • Convert the time series into sequence of events at each spatial location. Mining For Spatial Patterns

14. 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. Mining For Spatial Patterns

15. Association Rules FPAR-Hi  NPP-Hi (support  10) Shrubland regions • Intra-zone non-sequential Patterns • 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. Mining For Spatial Patterns

16. Co-location Can you find co-location patterns from the following sample dataset? Answers: and Mining For Spatial Patterns

17. Co-location Can you find co-location patterns from the following sample dataset? Mining For Spatial Patterns

18. 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 Tc = subsets of T frequently co-located Objective Correctness Completeness Efficiency Constraints R is symmetric and reflexive Monotonic prevalence measure Reference Feature Centric Window Centric Event Centric Mining For Spatial Patterns

19. Co-location Comparison with association rules 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 Mining For Spatial Patterns

20. 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 Mining For Spatial Patterns

21. 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=1 B,C=2 Support A,B =2 B,C=2 Mining For Spatial Patterns

22. 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 • Note: Neighbor relationship includes following pairs: • A1, B1 • A2, B1 • A2, B2 • B1, C1 • B2, C2 Spatial feature A,B, C, and their instances Mining For Spatial Patterns

23. Spatial Co-location Patterns • Dataset • 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 Spatial feature A,B, C, and their instances Mining For Spatial Patterns

24. Spatial Co-location Patterns • Partition approach • Our approach • Dataset Support(A,B)=min(2/2,3/3)=1 Spatial feature A,B, C, and their instances Support(B,C)=min(2/2,2/2)=1 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 Mining For Spatial Patterns

25. Spatial Outliers • Spatial Outlier: A data point that is extreme relative to it neighbors • Case Study: traffic stations different from neighbors [SIGKDD 2001] • 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 Mining For Spatial Patterns

26. 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 = {vi | vi V, vi is a spatial outlier} Objective Correctness: The attribute values of vi is extreme, compared with its neighbors Computational efficiency Constraints and ST are algebraic aggregate functions of and Computation cost dominated by I/O op. Mining For Spatial Patterns

27. 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) S(x) Mining For Spatial Patterns

28. 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 I/O cost Z-order Cell-Tree CCAM Mining For Spatial Patterns

29. 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 • Algebric tests Scatter Plot Original Data Our Approach Mining For Spatial Patterns

30. Graphical Spatial Tests Moran Scatter Plot Original Data Variogram Cloud Mining For Spatial Patterns

31. Location Prediction • Citations: IEEE Tran. on Multimedia2002, 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! Mining For Spatial Patterns

32. Location Prediction 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 Water depth Vegetation durability Mining For Spatial Patterns

33. Motivation and Framework Mining For Spatial Patterns

34. Solution Procedures • 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. Mining For Spatial Patterns

35. Evaluation • Linear Regression • Spatial Regression • Spatial model is better Mining For Spatial Patterns

36. Solution Procedures • 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] Mining For Spatial Patterns

37. Comparison • 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. Mining For Spatial Patterns

38. MRF vs. SAR Confusion Matrix: Spatial Confusion Matrix: Mining For Spatial Patterns

39. Experiment Design Mining For Spatial Patterns

40. 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 NZ=130 Mining For Spatial Patterns

41. 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) SAR Prediction (ADNP=8.63) NZ=76 NZ=80 Mining For Spatial Patterns

42. 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 Mining For Spatial Patterns

43. Reference • 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. • 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. • 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. • S. Shekhar, C.T. Lu, P. Zhang, “Detecting Graph-based Saptial Outlier”, Intelligent Data Analysis, To appear in Vol. 6(3), 2002 • S. Shekhar, S. Chawla, the book“Spatial Database: Concepts, Implementation and Trends”, Prentice Hall, 2002 • 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. • S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Modeling Spatial Dependencies for Mining Geospatial Data”, First SIAM International Conference on Data Mining, 2001. • 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. • 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) Mining For Spatial Patterns

44. Reference • S. Shekhar, C.T. Lu, P. Zhang, “A Unified Approach to Spatial Outliers Detection”, IEEE Transactions on Knowledge and Data Engineering (Submitted) • 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. • 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 • 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 Mining For Spatial Patterns