Efficient and Effective Clustering Methods for Spatial Data Mining

1. Efficient and Effective Clustering Methods for Spatial Data Mining Raymond T. Ng, Jiawei Han Pavan Podila COSC 6341, Fall ‘04

2. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

3. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

4. Spatial Data Mining • Identifying interesting relationships and characteristics that may exist implicitly in Spatial Databases • Different from Relational Databases • Spatial objects - store both spatial and non-spatial attributes • Queries (“All Walmart stores within 10 miles of UH) • Spatial Joins, work on spatial indexes (R-tree) • Huge sizes (Tera bytes) • GIS is a classic example

5. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

6. Partitioning Methods Given K, the number of partitions to create, a partitioning method constructs initial partitions. It then iterative refines the quality of these clusters so as to maximize intra-cluster similarity and inter-cluster dissimilarity. [Quality of Clustering]: Average dissimilarity of objects from their cluster centers (medoids) Selected algorithms: • K-medoids • PAM • CLARA • CLARANS

7. K-Medoids • Partition based clustering (K partitions) • Effective, why ? • Resistant to outliers • Do not depend on order in which data points are examined • Cluster center is part of dataset, unlike k-means where cluster center is gravity based • Experiments show that large data sets are handled efficiently K-medoids K-means

8. PAM (Partitioning Around Medoids) • [Goal]: Find K representative objects of the data set. Each of the K objects is called a Medoid, the most centrally located object within a cluster.

9. PAM (2) • Start with K data points designated as medoids. Create cluster around a medoid by moving data points close to the medoidOj belongs to Oi if d(Oj, Oi) = minOe d(Oj, Oe) • Iteratively replace Oi with Oh if quality of clustering improves. • Swapping cost, Cijh, associated for replacing a selected object Oi with a non-selected object Oh

10. PAM (3) • * O(k(n-k)2) for each iteration • * Good for small data sets (n=100, k=5)

11. CLARA (Clustering LARge Applications) • Improvement over PAM • Finds medoids in a sample from the dataset • [Idea]: If the samples are sufficiently random, the medoids of the sample approximate the medoids of the dataset • [Heuristics]: 5 samples of size 40+2k gives satisfactory results • Works well for large datasets (n=1000, k=10)

12. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

13. CLARANS (Clustering Large Applications based on RANdomized Search) • A graph abstraction, Gn,k • Each vertex is a collection of k medoids • | S1 S2 | = k – 1 • Each node has k(n-k) neighbors • Cost of each node is total dissimilarity of objects to their medoids • PAM searches whole graph • CLARA searches subgraph

14. CLARANS (2) • Experimental values • numLocal = 2 • maxNeighbors = • max(1.25% of k(n-k), 250)

15. CLARANS (3) • Outperforms PAM and CLARA in terms of running time and quality of clustering • O(n2) for each iteration CLARANS vs CLARA CLARANS vs PAM

16. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

17. Sphere(color, diameter) Initial relation Generalized relation Generalization • Useful to mine non-spatial attributes • Process of merging tuples based on a concept hierarchy • DBLearn – SQL query, gen. hierarchy and threshold

18. Silhouette Silhouette of object Oj • determines how much Oj belongs to it’s cluster • Between -1 and 1 • 1 indicates high degree of membership Silhouette width of cluster • Average silhouette of all objects in cluster Silhouette coefficient • Average silhouette widths of k clusters

19. SD and NSD approach • SD – Spatial Dominant • NSD – Non-Spatial Dominant • Clustering for spatial attributes / Generalization for non-spatial attributes • Dominance is decided by what is carried out first (clustering/generalization) • Second phase works on tuples from previous stage

20. SD(CLARANS) • Finds non-spatial generalizations from spatial clustering • Value for Knat is determined through heuristics using the silhouette coefficients • Clustering phase can be treated as finding spatial generalization hierarchy

21. NSD(CLARANS) • Finds spatial clusters from non-spatial generalizations • Clusters may overlap

22. Overview • Spatial Data Mining • Clustering techniques • CLARANS • Spatial and Non-Spatial dominant CLARANS • Observations • Summary

23. Observations • In all previous methods, quality of mining depends on the SQL query • CLARANS assumes that the entire dataset is in memory. Not always the case for large data sets. • Quality of results cannot be guaranteed when N is very large – due to Randomized Search

24. Observations (2) • Other clustering algorithms proposed for Spatial Data Mining • Hierarchical: BIRCH • Density based: DBSCAN, GDBSCAN, DBRS • Grid based: STING

25. Summary • A seminal paper on use of clustering for spatial data mining • CLARANS is an effective clustering technique for large datasets • SD(CLARANS)/NSD(CLARANS) are effective spatial data mining algorithms

26. References • Primary • Efficient and Effective Clustering Methods for Spatial Data Mining (1994) -Raymond T. Ng, Jiawei Han • Secondary • CLARANS: A Method for Clustering Objects for Spatial Data Mining -Raymond T. Ng, Jiawei Han • Clustering for Mining in Large Spatial Databases -Martin Ester, Hans-Peter Kriegel, Jörg Sander, Xiaowei Xu • An Introduction to Spatial Database Systems -Ralf Hartmut Güting