1. The UNIVERSITY of Kansas EECS 800 Research Seminar Mining Biological Data Instructor: Luke Huan Fall, 2006

2. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide2 10/02/2006 Subspace Clustering Administrative If you haven’t scheduled a meeting for the class project with the instructor, please do this asap.

3. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide3 10/02/2006 Subspace Clustering Overview Hierarchical clustering Density based clustering Graph based clustering Subspace clustering

4. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide4 10/02/2006 Subspace Clustering Hierarchical Clustering Use distance matrix as clustering criteria. This method does not require the number of clusters k as an input, but needs a termination condition Step 0 Step 1Step 2Step 3Step 4 b d c e a a b d e c d e a b c d e Step 4 Step 3Step 2Step 1Step 0 agglomerative (AGNES) divisive (DIANA)

5. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide5 10/02/2006 Subspace Clustering AGNES (Agglomerative Nesting) Introduced in Kaufmann and Rousseeuw (1990) Implemented in statistical analysis packages, e.g., Splus Use the Single-Link method and the dissimilarity matrix. Merge nodes that have the least dissimilarity Go on in a non-descending fashion Eventually all nodes belong to the same cluster

6. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide6 10/02/2006 Subspace Clustering Density-Based Clustering Methods Clustering based on density (local cluster criterion), such as density- connected points Major features: Discover clusters of arbitrary shape Handle noise One scan Need density parameters as termination condition Several studies: DBSCAN: Ester, et al. (KDD’96) OPTICS: Ankerst, et al (SIGMOD’99). DENCLUE: Hinneburg & D. Keim (KDD’98) CLIQUE: Agrawal, et al. (SIGMOD’98) (more grid-based)

7. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide7 10/02/2006 Subspace Clustering Density-Based Clustering: Basic Concepts Two parameters: Eps: Maximum radius of the neighbourhood MinPts: Minimum number of points in an Eps-neighbourhood of that point N Eps (p):{q belongs to D | dist(p,q) <= Eps} Directly density-reachable: A point p is directly density-reachable from a point q w.r.t. Eps, MinPts if p belongs to N Eps (q) core point condition: |N Eps (q)| >= MinPts Directly density-reachable is asymmetric p q MinPts = 5 Eps = 1 cm

8. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide8 10/02/2006 Subspace Clustering Density-Reachable and Density-Connected Density-reachable: A point p is density-reachable from a point q w.r.t. Eps, MinPts if there is a chain of points p 1, …, p n, p 1 = q, p n = p such that p i+1 is directly density-reachable from p i Density-connected A point p is density-connected to a point q w.r.t. Eps, MinPts if there is a point o such that both, p and q are density-reachable from o w.r.t. Eps and MinPts pq o p q p1p1

9. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide9 10/02/2006 Subspace Clustering DBSCAN: Density Based Spatial Clustering of Applications with Noise A cluster is a maximal set of density-connected points Discovers clusters of arbitrary shape in spatial databases with noise A point is a core point if it has more than a specified number of points (MinPts) within Eps. These are points that are at the interior of a cluster A border point has fewer than MinPts within Eps, but is in the neighborhood of a core point A noise point is any point that is not a core point or a border point. Core Border Outlier Eps = 1cm MinPts = 5

10. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide10 10/02/2006 Subspace Clustering DBSCAN: The Algorithm Classify all points to {core, border, noise} w.r.t. Eps and MinPts. Select a point P arbitrarily If p is a core point, a cluster is formed. If p is a border point, no points are density-reachable from p and DBSCAN visits the next point of the database. Continue the process until all of the points have been processed.

11. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide11 10/02/2006 Subspace Clustering DBSCAN Algorithm Eliminate noise points Perform clustering on the remaining points

12. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide12 10/02/2006 Subspace Clustering DBSCAN: Core, Border and Noise Points Original Points Point types: core, border and noise Eps = 10, MinPts = 4

13. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide13 10/02/2006 Subspace Clustering When DBSCAN Does NOT Work Well Original Points (MinPts=4, Eps=9.75). (MinPts=4, Eps=9.92) Varying densities High-dimensional data

14. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide14 10/02/2006 Subspace Clustering DBSCAN: Sensitive to Parameters

15. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide15 10/02/2006 Subspace Clustering OPTICS: A Cluster-Ordering Method (1999) OPTICS: Ordering Points To Identify the Clustering Structure Ankerst, Breunig, Kriegel, and Sander (SIGMOD’99) Produces a special order of the database w.r.t. its density-based clustering structure Good for both automatic and interactive cluster analysis, including finding intrinsic clustering structure Can be represented graphically or using visualization techniques This cluster-ordering contains info is equiv to the density-based clusterings that corresponds to a broad range of parameter settings (distance parameters)

16. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide16 10/02/2006 Subspace Clustering Core Distance MinPts-distance(p) for an object p is the distance between p and its MinPtrs neighbor. Core distance(p) is MinPts-distance(p) for a core object Core distance(p) is not defined for none core objects D

17. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide17 10/02/2006 Subspace Clustering Reachability Distance Reachability distance: The reachability-distance of an object p with respect to another core object o is the smallest distance such that p is directly density-reachable from o. For a pair of p and o (o is a core object): max(core-distance(o), distance(o, p)) p2 o p1

18. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide18 10/02/2006 Subspace Clustering Object Ordering Reachability- distance Cluster-order of the objects undefined ‘

19. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide19 10/02/2006 Subspace Clustering Density-Based Clustering: OPTICS & Its Applications

20. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide20 10/02/2006 Subspace Clustering DENCLUE: Using Statistical Density Functions Using statistical density estimations Major features Solid mathematical foundation Good for data sets with large amounts of noise Allows a compact mathematical description of arbitrarily shaped clusters in high-dimensional data sets Significant faster than existing algorithm (e.g., DBSCAN) But needs a large number of parameters An Efficient Approach to Clustering in Large Multimedia Databases with Noise by Hinneburg & Keim (KDD’98)

21. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide21 10/02/2006 Subspace Clustering Gradient: The steepness of a slope Example

22. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide22 10/02/2006 Subspace Clustering Example: Density Computation D={x1,x2,x3,x4} f D Gaussian (x)= influence(x1) + influence(x2) + influence(x3) + influence(x4)=0.04+0.06+0.08+0.6=0.78 x1 x2 x3 x4 x 0.6 0.08 0.06 0.04 y Remark: the density value of y would be larger than the one for x

23. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide23 10/02/2006 Subspace Clustering Uses grid cells but only keeps information about grid cells that do actually contain data points and manages these cells in a tree-based access structure Influence function: describes the impact of a data point within its neighborhood Overall density of the data space can be calculated as the sum of the influence function of all data points Clusters can be determined mathematically by identifying density attractors Density attractors are local maximal of the overall density function Denclue: Technical Essence

24. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide24 10/02/2006 Subspace Clustering Density Attractor

25. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide25 10/02/2006 Subspace Clustering Center-Defined and Arbitrary

26. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide26 10/02/2006 Subspace Clustering Graph-Based Clustering Graph-Based clustering uses the proximity graph Start with the proximity matrix Consider each point as a node in a graph Each edge between two nodes has a weight which is the proximity between the two points Initially the proximity graph is fully connected MIN (single-link) and MAX (complete-link) can be viewed as starting with this graph In the simplest case, clusters are connected components in the graph.

27. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide27 10/02/2006 Subspace Clustering Graph-Based Clustering: Sparsification The amount of data that needs to be processed is drastically reduced Sparsification can eliminate more than 99% of the entries in a proximity matrix The amount of time required to cluster the data is drastically reduced The size of the problems that can be handled is increased

28. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide28 10/02/2006 Subspace Clustering Graph-Based Clustering: Sparsification … Clustering may work better Sparsification techniques keep the connections to the most similar (nearest) neighbors of a point while breaking the connections to less similar points. The nearest neighbors of a point tend to belong to the same class as the point itself. This reduces the impact of noise and outliers and sharpens the distinction between clusters. Sparsification facilitates the use of graph partitioning algorithms (or algorithms based on graph partitioning algorithms. Chameleon and Hypergraph-based Clustering

29. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide29 10/02/2006 Subspace Clustering Sparsification in the Clustering Process

30. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide30 10/02/2006 Subspace Clustering Chameleon: Clustering Using Dynamic Modeling Adapt to the characteristics of the data set to find the natural clusters Use a dynamic model to measure the similarity between clusters Main property is the relative closeness and relative inter-connectivity of the cluster Two clusters are combined if the resulting cluster shares certain properties with the constituent clusters The merging scheme preserves self-similarity One of the areas of application is spatial data

31. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide31 10/02/2006 Subspace Clustering Characteristics of Spatial Data Sets The clustering algorithm must address the above characteristics and also require minimal supervision. Clusters are defined as densely populated regions of the space Clusters have arbitrary shapes, orientation, and non-uniform sizes Difference in densities across clusters and variation in density within clusters Existence of special artifacts and noise

32. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide32 10/02/2006 Subspace Clustering Chameleon: Steps Preprocessing Step: Represent the Data by a Graph Given a set of points, construct the k-nearest-neighbor (k-NN) graph to capture the relationship between a point and its k nearest neighbors Concept of neighborhood is captured dynamically (even if region is sparse) Phase 1: Use a multilevel graph partitioning algorithm on the graph to find a large number of clusters of well- connected vertices Each cluster should contain mostly points from one “true” cluster, i.e., is a sub-cluster of a “real” cluster

33. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide33 10/02/2006 Subspace Clustering Chameleon: Steps … Phase 2: Use Hierarchical Agglomerative Clustering to merge sub- clusters Two clusters are combined if the resulting cluster shares certain properties with the constituent clusters Two key properties used to model cluster similarity: Relative Interconnectivity: Absolute interconnectivity of two clusters normalized by the internal connectivity of the clusters Relative Closeness: Absolute closeness of two clusters normalized by the internal closeness of the clusters CHAMELEON measures the closeness of two clusters by computing the average similarity between the points in C i that are connected to points in C j

34. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide34 10/02/2006 Subspace Clustering CHAMELEON (Clustering Complex Objects)

35. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide35 10/02/2006 Subspace Clustering Grid-Based Clustering Method Using multi-resolution grid data structure Several interesting methods STING (a STatistical INformation Grid approach) by Wang, Yang and Muntz (1997) WaveCluster by Sheikholeslami, Chatterjee, and Zhang (VLDB’98) A multi-resolution clustering approach using wavelet method CLIQUE: Agrawal, et al. (SIGMOD’98) On high-dimensional data (thus put in the section of clustering high-dimensional data

36. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide36 10/02/2006 Subspace Clustering STING: A Statistical Information Grid Approach Wang, Yang and Muntz (VLDB’97) The spatial area area is divided into rectangular cells There are several levels of cells corresponding to different levels of resolution

37. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide37 10/02/2006 Subspace Clustering The STING Clustering Method Each cell at a high level is partitioned into a number of smaller cells in the next lower level Statistical info of each cell is calculated and stored beforehand and is used to answer queries Parameters of higher level cells can be easily calculated from parameters of lower level cell count, mean, s, min, max type of distribution—normal, uniform, etc. Use a top-down approach to answer spatial data queries Start from a pre-selected layer — typically with a small number of cells For each cell in the current level compute the confidence interval

38. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide38 10/02/2006 Subspace Clustering Comments on STING Remove the irrelevant cells from further consideration When finish examining the current layer, proceed to the next lower level Repeat this process until the bottom layer is reached Advantages: Query-independent, easy to parallelize, incremental update O(K), where K is the number of grid cells at the lowest level Disadvantages: All the cluster boundaries are either horizontal or vertical, and no diagonal boundary is detected

39. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide39 10/02/2006 Subspace Clustering WaveCluster: Clustering by Wavelet Analysis (1998) Sheikholeslami, Chatterjee, and Zhang (VLDB’98) A multi-resolution clustering approach which applies wavelet transform to the feature space How to apply wavelet transform to find clusters Summarizes the data by imposing a multidimensional grid structure onto data space These multidimensional spatial data objects are represented in a n-dimensional feature space Apply wavelet transform on feature space to find the dense regions in the feature space Apply wavelet transform multiple times which result in clusters at different scales from fine to coarse

40. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide40 10/02/2006 Subspace Clustering Wavelet Transform Wavelet transform: A signal processing technique that decomposes a signal into different frequency sub-band (can be applied to n- dimensional signals) Data are transformed to preserve relative distance between objects at different levels of resolution Allows natural clusters to become more distinguishable

41. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide41 10/02/2006 Subspace Clustering The WaveCluster Algorithm Input parameters # of grid cells for each dimension the wavelet, and the # of applications of wavelet transform Why is wavelet transformation useful for clustering? Use hat-shape filters to emphasize region where points cluster, but simultaneously suppress weaker information in their boundary Effective removal of outliers, multi-resolution, cost effective Major features: Detect arbitrary shaped clusters at different scales Not sensitive to noise, not sensitive to input order Only applicable to low dimensional data Both grid-based and density-based

42. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide42 10/02/2006 Subspace Clustering Quantization & Transformation First, quantize data into m-D grid structure, then wavelet transform a) scale 1: high resolution b) scale 2: medium resolution c) scale 3: low resolution

43. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide43 10/02/2006 Subspace Clustering Clustering High-Dimensional Data Clustering high-dimensional data Many applications: text documents, DNA micro-array data Major challenges: Many irrelevant dimensions may mask clusters Distance measure becomes meaningless—due to equi-distance Clusters may exist only in some subspaces

44. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide44 10/02/2006 Subspace Clustering Clustering in High Dimensional Space Methods Feature transformation: only effective if most dimensions are relevant PCA & SVD useful only when features are highly correlated/redundant Feature selection: wrapper or filter approaches useful to find a subspace where the data have nice clusters Subspace-clustering: find clusters in all the possible subspaces CLIQUE, ProClus, and frequent pattern-based clustering

45. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide45 10/02/2006 Subspace Clustering The Curse of Dimensionality (graphs adapted from Parsons et al. KDD Explorations 2004) Data in only one dimension is relatively packed Adding a dimension “stretch” the points across that dimension, making them further apart Density decrease dramatically Distance measure becomes meaningless — due to equi-distance

46. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide46 10/02/2006 Subspace Clustering Why Subspace Clustering? (adapted from Parsons et al. SIGKDD Explorations 2004) Clusters may exist only in some subspaces Subspace-clustering: find clusters in all the subspaces

47. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide47 10/02/2006 Subspace Clustering CLIQUE (Clustering In QUEst) Agrawal, Gehrke, Gunopulos, Raghavan (SIGMOD’98) Automatically identifying subspaces of a high dimensional data space that allow better clustering than original space CLIQUE can be considered as both density-based and grid-based It partitions each dimension into the same number of equal length interval It partitions an m-dimensional data space into non-overlapping rectangular units A unit is dense if the fraction of total data points contained in the unit exceeds the input model parameter A cluster is a maximal set of connected dense units within a subspace

48. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide48 10/02/2006 Subspace Clustering CLIQUE: The Major Steps Partition the data space and find the number of points that lie inside each cell of the partition. Identify the subspaces that contain clusters using the Apriori principle Identify clusters Determine dense units in all subspaces of interests Determine connected dense units in all subspaces of interests. Generate minimal description for the clusters Determine maximal regions that cover a cluster of connected dense units for each cluster Determination of minimal cover for each cluster

49. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide49 10/02/2006 Subspace Clustering Salary (10,000 ) 2030405060 age 5 4 3 1 2 6 7 0 2030405060 age 5 4 3 1 2 6 7 0 Vacatio n(week) age Vacatio n Salar y 3050  = 3

50. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide50 10/02/2006 Subspace Clustering Strength and Weakness of CLIQUE Strength automatically finds subspaces of the highest dimensionality such that high density clusters exist in those subspaces insensitive to the order of records in input and does not presume some canonical data distribution scales linearly with the size of input and has good scalability as the number of dimensions in the data increases Weakness The accuracy of the clustering result may be degraded at the expense of simplicity of the method

51. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide51 10/02/2006 Subspace Clustering Frequent Pattern-Based Approach Clustering high-dimensional space (e.g., clustering text documents, microarray data) Projected subspace-clustering: which dimensions to be projected on? CLIQUE, ProClus Feature extraction: costly and may not be effective? Using frequent patterns as “features” “Frequent” are inherent features Mining freq. patterns may not be so expensive

52. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide52 10/02/2006 Subspace Clustering Summary Cluster analysis groups objects based on their similarity and has wide applications Measure of similarity can be computed for various types of data Clustering algorithms can be categorized into partitioning methods, hierarchical methods, density-based methods, grid-based methods, and model-based methods Outlier detection and analysis are very useful for fraud detection, etc. and can be performed by statistical, distance-based or deviation- based approaches There are still lots of research issues on cluster analysis

53. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide53 10/02/2006 Subspace Clustering Problems and Challenges Considerable progress has been made in scalable clustering methods Partitioning: k-means, k-medoids, CLARANS Hierarchical: BIRCH, ROCK, CHAMELEON Density-based: DBSCAN, OPTICS, DenClue Grid-based: STING, WaveCluster, CLIQUE Model-based: EM, Cobweb, SOM Frequent pattern-based: pCluster Current clustering techniques do not address all the requirements adequately, still an active area of research

54. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide54 10/02/2006 Subspace Clustering References (1) R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan. Automatic subspace clustering of high dimensional data for data mining applications. SIGMOD'98 M. R. Anderberg. Cluster Analysis for Applications. Academic Press, 1973. M. Ankerst, M. Breunig, H.-P. Kriegel, and J. Sander. Optics: Ordering points to identify the clustering structure, SIGMOD’99. P. Arabie, L. J. Hubert, and G. De Soete. Clustering and Classification. World Scientific, 1996 Beil F., Ester M., Xu X.: "Frequent Term-Based Text Clustering", KDD'02Frequent Term-Based Text Clustering M. M. Breunig, H.-P. Kriegel, R. Ng, J. Sander. LOF: Identifying Density-Based Local Outliers. SIGMOD 2000. M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases. KDD'96. M. Ester, H.-P. Kriegel, and X. Xu. Knowledge discovery in large spatial databases: Focusing techniques for efficient class identification. SSD'95. D. Fisher. Knowledge acquisition via incremental conceptual clustering. Machine Learning, 2:139-172, 1987. D. Gibson, J. Kleinberg, and P. Raghavan. Clustering categorical data: An approach based on dynamic systems. VLDB’98.

55. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide55 10/02/2006 Subspace Clustering References (2) V. Ganti, J. Gehrke, R. Ramakrishan. CACTUS Clustering Categorical Data Using Summaries. KDD'99. D. Gibson, J. Kleinberg, and P. Raghavan. Clustering categorical data: An approach based on dynamic systems. In Proc. VLDB’98. S. Guha, R. Rastogi, and K. Shim. Cure: An efficient clustering algorithm for large databases. SIGMOD'98. S. Guha, R. Rastogi, and K. Shim. ROCK: A robust clustering algorithm for categorical attributes. In ICDE'99, pp. 512-521, Sydney, Australia, March 1999.ROCK: A robust clustering algorithm for categorical attributes A. Hinneburg, D.l A. Keim: An Efficient Approach to Clustering in Large Multimedia Databases with Noise. KDD’98. A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Printice Hall, 1988. G. Karypis, E.-H. Han, and V. Kumar. CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling. COMPUTER, 32(8): 68-75, 1999.CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling. L. Kaufman and P. J. Rousseeuw. Finding Groups in Data: an Introduction to Cluster Analysis. John Wiley & Sons, 1990. E. Knorr and R. Ng. Algorithms for mining distance-based outliers in large datasets. VLDB’98. G. J. McLachlan and K.E. Bkasford. Mixture Models: Inference and Applications to Clustering. John Wiley and Sons, 1988. P. Michaud. Clustering techniques. Future Generation Computer systems, 13, 1997. R. Ng and J. Han. Efficient and effective clustering method for spatial data mining. VLDB'94.

56. Mining Biological Data KU EECS 800, Luke Huan, Fall’06 slide56 10/02/2006 Subspace Clustering References (3) L. Parsons, E. Haque and H. Liu, Subspace Clustering for High Dimensional Data: A Review, SIGKDD Explorations, 6(1), June 2004Subspace Clustering for High Dimensional Data: A Review E. Schikuta. Grid clustering: An efficient hierarchical clustering method for very large data sets. Proc. 1996 Int. Conf. on Pattern Recognition,. G. Sheikholeslami, S. Chatterjee, and A. Zhang. WaveCluster: A multi-resolution clustering approach for very large spatial databases. VLDB’98. A. K. H. Tung, J. Han, L. V. S. Lakshmanan, and R. T. Ng. Constraint-Based Clustering in Large Databases, ICDT'01.Constraint-Based Clustering in Large Databases A. K. H. Tung, J. Hou, and J. Han. Spatial Clustering in the Presence of Obstacles, ICDE'01Spatial Clustering in the Presence of Obstacles H. Wang, W. Wang, J. Yang, and P.S. Yu. Clustering by pattern similarity in large data sets, SIGMOD’ 02.Clustering by pattern similarity in large data sets W. Wang, Yang, R. Muntz, STING: A Statistical Information grid Approach to Spatial Data Mining, VLDB’97. T. Zhang, R. Ramakrishnan, and M. Livny. BIRCH : an efficient data clustering method for very large databases. SIGMOD'96.