Data Mining Cluster Analysis Basic Concepts and Algorithms Lecture Notes for Chapter 8 Introduction to Data Mining by Tan Steinbach Kumar Introduction to Data Mining 4 18 2004 1 What is Cluster Analysis Finding groups of objects such that the objects in a group will be similar or related to one another and different from or unrelated to the objects in other groups Intra cluster distances are minimized Introduction to Data Mining Inter cluster distances are maximized 4 18 2004 2 Applications of Cluster Analysis Understanding Group related documents for browsing group genes and proteins that have similar functionality or group stocks with similar price fluctuations Summarization Reduce the size of large data sets Clustering precipitation in Australia Introduction to Data Mining 4 18 2004 3 What is not Cluster Analysis Supervised classification Have class label information Simple segmentation Dividing students into different registration groups alphabetically by last name Results of a query Groupings are a result of an external specification Graph partitioning Some mutual relevance and synergy but areas are not identical Introduction to Data Mining 4 18 2004 4 Notion of a Cluster can be Ambiguous How many clusters Six Clusters Two Clusters Four Clusters Introduction to Data Mining 4 18 2004 5 Types of Clusterings A clustering is a set of clusters Important distinction between hierarchical and partitional sets of clusters Partitional Clustering A division data objects into non overlapping subsets clusters such that each data object is in exactly one subset Hierarchical clustering A set of nested clusters organized as a hierarchical tree Introduction to Data Mining 4 18 2004 6 Partitional Clustering Original Points Introduction to Data Mining A Partitional Clustering 4 18 2004 7 Hierarchical Clustering p1 p3 p4 p2 p1 p2 Traditional Hierarchical Clustering p1 p3 p3 p4 Traditional Dendrogram p4 p2 p1 p2 Non traditional Hierarchical Clustering Introduction to Data Mining p3 p4 Non traditional Dendrogram 4 18 2004 8 Other Distinctions Between Sets of Clusters Exclusive versus non exclusive In non exclusive clusterings points may belong to multiple clusters Can represent multiple classes or border points Fuzzy versus non fuzzy In fuzzy clustering a point belongs to every cluster with some weight between 0 and 1 Weights must sum to 1 Probabilistic clustering has similar characteristics Partial versus complete In some cases we only want to cluster some of the data Heterogeneous versus homogeneous Cluster of widely different sizes shapes and densities Introduction to Data Mining 4 18 2004 9 Types of Clusters Well separated clusters Center based clusters Contiguous clusters Density based clusters Property or Conceptual Described by an Objective Function Introduction to Data Mining 4 18 2004 10 Types of Clusters Well Separated Well Separated Clusters A cluster is a set of points such that any point in a cluster is closer or more similar to every other point in the cluster than to any point not in the cluster 3 well separated clusters Introduction to Data Mining 4 18 2004 11 Types of Clusters Center Based Center based A cluster is a set of objects such that an object in a cluster is closer more similar to the center of a cluster than to the center of any other cluster The center of a cluster is often a centroid the average of all the points in the cluster or a medoid the most representative point of a cluster 4 center based clusters Introduction to Data Mining 4 18 2004 12 Types of Clusters Contiguity Based Contiguous Cluster Nearest neighbor or Transitive A cluster is a set of points such that a point in a cluster is closer or more similar to one or more other points in the cluster than to any point not in the cluster 8 contiguous clusters Introduction to Data Mining 4 18 2004 13 Types of Clusters Density Based Density based A cluster is a dense region of points which is separated by low density regions from other regions of high density Used when the clusters are irregular or intertwined and when noise and outliers are present 6 density based clusters Introduction to Data Mining 4 18 2004 14 Types of Clusters Conceptual Clusters Shared Property or Conceptual Clusters Finds clusters that share some common property or represent a particular concept 2 Overlapping Circles Introduction to Data Mining 4 18 2004 15 Types of Clusters Objective Function Clusters Defined by an Objective Function Finds clusters that minimize or maximize an objective function Enumerate all possible ways of dividing the points into clusters and evaluate the goodness of each potential set of clusters by using the given objective function NP Hard Can have global or local objectives Hierarchical clustering algorithms typically have local objectives Partitional algorithms typically have global objectives A variation of the global objective function approach is to fit the data to a parameterized model Parameters for the model are determined from the data Mixture models assume that the data is a mixture of a number of statistical distributions Introduction to Data Mining 4 18 2004 16 Types of Clusters Objective Function Map the clustering problem to a different domain and solve a related problem in that domain Proximity matrix defines a weighted graph where the nodes are the points being clustered and the weighted edges represent the proximities between points Clustering is equivalent to breaking the graph into connected components one for each cluster Want to minimize the edge weight between clusters and maximize the edge weight within clusters Introduction to Data Mining 4 18 2004 17 Characteristics of the Input Data Are Important Type of proximity or density measure This is a derived measure but central to clustering Sparseness Dictates type of similarity Adds to efficiency Attribute type Dictates type of similarity Type of Data Dictates type of similarity Other characteristics e g autocorrelation Dimensionality Noise and Outliers Type of Distribution Introduction to Data Mining 4 18 2004 18 Clustering Algorithms K means and its variants Hierarchical clustering Density based clustering Introduction to Data Mining 4 18 2004 19 K means Clustering Partitional clustering approach Each cluster is associated with a centroid center point Each point is assigned to the cluster with the closest centroid Number of clusters K must be specified The basic algorithm is very simple Introduction to Data Mining 4 18 2004 20 K means
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