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Data Mining: Concepts and Techniques Clustering

Data Mining: Concepts and Techniques Clustering. Chapter 8. Cluster Analysis. What is Cluster Analysis? Types of Data in Cluster Analysis A Categorization of Major Clustering Methods Partitioning Methods Hierarchical Methods Density-Based Methods Grid-Based Methods Outlier Analysis

jerry-ellison
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Data Mining: Concepts and Techniques Clustering

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  1. Data Mining: Concepts and TechniquesClustering Data Mining: Concepts and Techniques

  2. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  3. What is Cluster Analysis? • Cluster: a collection of data objects • Similar to one another within the same cluster • Dissimilar to the objects in other clusters • Cluster analysis • Grouping a set of data objects into clusters • Clustering is unsupervised classification: no predefined classes • Typical applications • As a stand-alone tool to get insight into data distribution • As a preprocessing step for other algorithms

  4. General Applications of Clustering • Pattern Recognition • Spatial Data Analysis • create thematic maps in GIS by clustering feature spaces • detect spatial clusters and explain them in spatial data mining • Image Processing • Economic Science (especially market research) • WWW • Document classification • Cluster Weblog data to discover groups of similar access patterns Data Mining: Concepts and Techniques

  5. Examples of Clustering Applications • Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs • Land use: Identification of areas of similar land use in an earth observation database • Insurance: Identifying groups of motor insurance policy holders with a high average claim cost • City-planning: Identifying groups of houses according to their house type, value, and geographical location • Earth-quake studies: Observed earth quake epicenters should be clustered along continent faults Data Mining: Concepts and Techniques

  6. What Is Good Clustering? • A good clustering method will produce high quality clusters with • high intra-class similarity • low inter-class similarity • The quality of a clustering result depends on both the similarity measure used by the method and its implementation. • The quality of a clustering method is also measured by its ability to discover some or all of the hidden patterns. Data Mining: Concepts and Techniques

  7. Requirements of Clustering in Data Mining • Scalability • Ability to deal with different types of attributes • Discovery of clusters with arbitrary shape • Minimal requirements for domain knowledge to determine input parameters • Able to deal with noise and outliers • Insensitive to order of input records • High dimensionality • Incorporation of user-specified constraints • Interpretability and usability Data Mining: Concepts and Techniques

  8. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  9. Data Structures • Data matrix • (two modes) • Dissimilarity matrix • (one mode) Data Mining: Concepts and Techniques

  10. Measure the Quality of Clustering • Dissimilarity/Similarity metric: Similarity is expressed in terms of a distance function, which is typically metric: d(i, j) • There is a separate “quality” function that measures the “goodness” of a cluster. • The definitions of distance functions are usually very different for interval-scaled, boolean, categorical, ordinal and ratio variables. • Weights should be associated with different variables based on applications and data semantics. • It is hard to define “similar enough” or “good enough” • the answer is typically highly subjective. Data Mining: Concepts and Techniques

  11. Type of data in clustering analysis • Interval-scaled variables • Binary variables • Nominal, ordinal, and ratio variables • Variables of mixed types Data Mining: Concepts and Techniques

  12. Interval-valued variables • Standardize data • Calculate the mean absolute deviation: where • Calculate the standardized measurement (z-score) • Using mean absolute deviation is more robust than using standard deviation Data Mining: Concepts and Techniques

  13. Similarity and Dissimilarity Between Objects • Distances are normally used to measure the similarity or dissimilarity between two data objects • Some popular ones include: Minkowski distance: where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two p-dimensional data objects, and q is a positive integer • If q = 1, d is Manhattan distance Data Mining: Concepts and Techniques

  14. Similarity and Dissimilarity Between Objects (Cont.) • If q = 2, d is Euclidean distance: • Properties • d(i,j) 0 • d(i,i)= 0 • d(i,j)= d(j,i) • d(i,j) d(i,k)+ d(k,j) • Also one can use weighted distance, parametric Pearson product moment correlation, or other dissimilarity measures. Data Mining: Concepts and Techniques

  15. Binary Variables Object j • A contingency table for binary data • Simple matching coefficient (if the binary variable is symmetric): • Jaccard coefficient (if the binary variable is asymmetric): Object i Data Mining: Concepts and Techniques

  16. Dissimilarity Between Binary Variables: Example • gender is a symmetric attribute, the remaining attributes are asymmetric • let the values Y and P be set to 1, and the value N be set to 0 • consider only asymmetric attributes Data Mining: Concepts and Techniques

  17. Nominal Variables • A generalization of the binary variable in that it can take more than 2 states, e.g., red, yellow, blue, green • Method 1: Simple matching • m: # of matches, p: total # of variables • Method 2: use a large number of binary variables • creating a new binary variable for each of the M nominal states Data Mining: Concepts and Techniques

  18. Ordinal Variables • An ordinal variable can be discrete or continuous • Order is important, e.g., rank • Can be treated like interval-scaled • replacing xif by their rank • map the range of each variable onto [0, 1] by replacing i-th object in the f-th variable by • compute the dissimilarity using methods for interval-scaled variables Data Mining: Concepts and Techniques

  19. Ratio-Scaled Variables • Ratio-scaled variable: a positive measurement on a nonlinear scale, approximately at exponential scale, such as AeBt or Ae-Bt • Methods: • treat them like interval-scaled variables • apply logarithmic transformation yif = log(xif) • treat them as continuous ordinal data treat their rank as interval-scaled. Data Mining: Concepts and Techniques

  20. Variables of Mixed Types • A database may contain all the six types of variables • symmetric binary, asymmetric binary, nominal, ordinal, interval and ratio. • One may use a weighted formula to combine their effects. • f is binary or nominal: dij(f) = 0 if xif = xjf , or dij(f) = 1 otherwise • f is interval-based: use the normalized distance • f is ordinal or ratio-scaled • compute ranks rif and and treat zif as interval-scaled Data Mining: Concepts and Techniques

  21. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  22. Major Clustering Approaches • Partitioning algorithms: Construct various partitions and then evaluate them by some criterion • Hierarchy algorithms: Create a hierarchical decomposition of the set of data (or objects) using some criterion • Density-based: based on connectivity and density functions • Grid-based: based on a multiple-level granularity structure • Model-based: A model is hypothesized for each of the clusters and the idea is to find the best fit of that model to each other Data Mining: Concepts and Techniques

  23. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  24. Partitioning Algorithms: Basic Concept • Partitioning method: Construct a partition of a database D of n objects into a set of k clusters • Given k, find a partition of k clusters that optimizes the chosen partitioning criterion • Global optimality: exhaustively enumerate all partitions • Heuristic methods: k-means and k-medoids algorithms • k-means (MacQueen’67): Each cluster is represented by the center of the cluster • k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster Data Mining: Concepts and Techniques

  25. The K-Means Clustering Method • Given k, the k-means algorithm is implemented in 4 steps: • Partition objects into k nonempty subsets • Compute seed points as the centroids of the clusters of the current partition. The centroid is the center (mean point) of the cluster. • Assign each object to the cluster with the nearest seed point. • Go back to Step 2, stop when no more new assignment. Data Mining: Concepts and Techniques

  26. The K-Means Clustering Method • Example Data Mining: Concepts and Techniques

  27. Comments on the K-Means Method • Strength • Relatively efficient: O(tkn), where n is # objects, k is # clusters, and t is # iterations. Normally, k, t << n. • Often terminates at a local optimum. The global optimum may be found using techniques such as: deterministic annealing and genetic algorithms • Weakness • Applicable only when mean is defined, then what about categorical data? • Need to specify k, the number of clusters, in advance • Unable to handle noisy data and outliers • Not suitable to discover clusters with non-convex shapes Data Mining: Concepts and Techniques

  28. Variations of the K-Means Method • A few variants of the k-means which differ in • Selection of the initial k means • Dissimilarity calculations • Strategies to calculate cluster means • Handling categorical data: k-modes • Replacing means of clusters with modes • Using new dissimilarity measures to deal with categorical objects • Using a frequency-based method to update modes of clusters • A mixture of categorical and numerical data: k-prototype method Data Mining: Concepts and Techniques

  29. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  30. Step 0 Step 1 Step 2 Step 3 Step 4 agglomerative (AGNES) a a b b a b c d e c c d e d d e e divisive (DIANA) Step 3 Step 2 Step 1 Step 0 Step 4 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 Data Mining: Concepts and Techniques

  31. More on Hierarchical Clustering Methods • Major weakness of agglomerative clustering methods • do not scale well: time complexity of at least O(n2), where n is the number of total objects • can never undo what was done previously • Integration of hierarchical with distance-based clustering • BIRCH (1996): uses CF-tree and incrementally adjusts the quality of sub-clusters • CURE (1998): selects well-scattered points from the cluster and then shrinks them towards the center of the cluster by a specified fraction • CHAMELEON (1999): hierarchical clustering using dynamic modeling Data Mining: Concepts and Techniques

  32. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  33. 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 interesting 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) Data Mining: Concepts and Techniques

  34. Density Concepts • Core object (CO) – object with at least ‘M’ objects within a radius ‘E-neighborhood’ • Directly density reachable (DDR) – x is CO, y is in x’s ‘E-neighborhood’ • Density reachable – there exists a chain of DDR objects from x to y • Density based cluster – set of density connected objects that is maximal w.r.t. density-reachability Data Mining: Concepts and Techniques

  35. p MinPts = 5 Eps = 1 cm q Density-Based Clustering: Background • Two parameters: • Eps: Maximum radius of the neighbourhood • MinPts: Minimum number of points in an Eps-neighbourhood of that point • NEps(p): {q belongs to D | dist(p,q) <= Eps} • Directly density-reachable: A point p is directly density-reachable from a point q wrt. Eps, MinPts if • 1) p belongs to NEps(q) • 2) core point condition: |NEps (q)| >= MinPts Data Mining: Concepts and Techniques

  36. p q o Density-Based Clustering: Background (II) • Density-reachable: • A point p is density-reachable from a point q wrt. Eps, MinPts if there is a chain of points p1, …, pn, p1 = q, pn = p such that pi+1 is directly density-reachable from pi • Density-connected • A point p is density-connected to a point q wrt. Eps, MinPts if there is a point o such that both, p and q are density-reachable from o wrt. Eps and MinPts. p p1 q Data Mining: Concepts and Techniques

  37. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  38. What Is Outlier Discovery? • What are outliers? • The set of objects are considerably dissimilar from the remainder of the data • Example: Sports: Michael Jordon, Wayne Gretzky, ... • Problem • Find top n outlier points • Applications: • Credit card fraud detection • Telecom fraud detection • Customer segmentation • Medical analysis Data Mining: Concepts and Techniques

  39. Outlier Discovery: Statistical Approaches • Assume a model underlying distribution that generates data set (e.g. normal distribution) • Use discordancy tests depending on • data distribution • distribution parameter (e.g., mean, variance) • number of expected outliers • Drawbacks • most tests are for single attribute • in many cases, data distribution may not be known Data Mining: Concepts and Techniques

  40. Outlier Discovery: Distance-Based Approach • Introduced to counter the main limitations imposed by statistical methods • We need multi-dimensional analysis without knowing data distribution. • Distance-based outlier: A DB(p, D)-outlier is an object O in a dataset T such that at least a fraction p of the objects in T lies at a distance greater than D from O • Algorithms for mining distance-based outliers • Index-based algorithm • Nested-loop algorithm • Cell-based algorithm

  41. Chapter 8. Cluster Analysis • What is Cluster Analysis? • Types of Data in Cluster Analysis • A Categorization of Major Clustering Methods • Partitioning Methods • Hierarchical Methods • Density-Based Methods • Grid-Based Methods • Outlier Analysis • Summary Data Mining: Concepts and Techniques

  42. 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, such as constraint-based clustering Data Mining: Concepts and Techniques

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