Data Mining Cluster Analysis: Basic Concepts and AlgorithmsWhat is Cluster Analysis?Applications of Cluster AnalysisWhat is not Cluster Analysis?Notion of a Cluster can be AmbiguousTypes of ClusteringsPartitional ClusteringHierarchical ClusteringOther Distinctions Between Sets of ClustersTypes of ClustersTypes of Clusters: Well-SeparatedTypes of Clusters: Center-BasedTypes of Clusters: Contiguity-BasedTypes of Clusters: Density-BasedTypes of Clusters: Conceptual ClustersTypes of Clusters: Objective FunctionTypes of Clusters: Objective Function …Characteristics of the Input Data Are ImportantClustering AlgorithmsK-means ClusteringK-means Clustering – DetailsTwo different K-means ClusteringsImportance of Choosing Initial CentroidsSlide 24Evaluating K-means ClustersImportance of Choosing Initial Centroids …Slide 27Problems with Selecting Initial Points10 Clusters ExampleSlide 30Slide 31Slide 32Solutions to Initial Centroids ProblemHandling Empty ClustersUpdating Centers IncrementallyPre-processing and Post-processingBisecting K-meansBisecting K-means ExampleLimitations of K-meansLimitations of K-means: Differing SizesLimitations of K-means: Differing DensityLimitations of K-means: Non-globular ShapesOvercoming K-means LimitationsSlide 44Slide 45Hierarchical ClusteringStrengths of Hierarchical ClusteringSlide 48Agglomerative Clustering AlgorithmStarting SituationIntermediate SituationSlide 52After MergingHow to Define Inter-Cluster SimilaritySlide 55Slide 56Slide 57Slide 58Cluster Similarity: MIN or Single LinkHierarchical Clustering: MINStrength of MINLimitations of MINCluster Similarity: MAX or Complete LinkageHierarchical Clustering: MAXStrength of MAXLimitations of MAXCluster Similarity: Group AverageHierarchical Clustering: Group AverageSlide 69Cluster Similarity: Ward’s MethodHierarchical Clustering: ComparisonHierarchical Clustering: Time and Space requirementsHierarchical Clustering: Problems and LimitationsCluster ValidityClusters found in Random DataDifferent Aspects of Cluster ValidationMeasures of Cluster ValidityMeasuring Cluster Validity Via CorrelationSlide 79Using Similarity Matrix for Cluster ValidationSlide 81Slide 82Slide 83Slide 84Internal Measures: SSESlide 86Framework for Cluster ValidityStatistical Framework for SSEStatistical Framework for CorrelationInternal Measures: Cohesion and SeparationSlide 91Slide 92Internal Measures: Silhouette CoefficientExternal Measures of Cluster Validity: Entropy and PurityFinal Comment on Cluster ValidityData MiningCluster Analysis: Basic Concepts and AlgorithmsLecture Notes for Chapter 8Introduction to Data MiningbyTan, Steinbach, Kumar Introduction to Data Mining 4/18/2004 1Introduction to Data Mining 4/18/2004 2 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 groupsInter-cluster distances are maximizedIntra-cluster distances are minimizedIntroduction to Data Mining 4/18/2004 3 Applications of Cluster AnalysisUnderstanding–Group related documents for browsing, group genes and proteins that have similar functionality, or group stocks with similar price fluctuationsSummarization–Reduce the size of large data setsClustering precipitation in AustraliaIntroduction to Data Mining 4/18/2004 4 What is not Cluster Analysis?Supervised classification–Have class label informationSimple segmentation–Dividing students into different registration groups alphabetically, by last nameResults of a query–Groupings are a result of an external specificationGraph partitioning–Some mutual relevance and synergy, but areas are not identicalIntroduction to Data Mining 4/18/2004 5 Notion of a Cluster can be AmbiguousHow many clusters?Four Clusters Two Clusters Six ClustersIntroduction to Data Mining 4/18/2004 6 Types of ClusteringsA clustering is a set of clustersImportant 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 subsetHierarchical clustering–A set of nested clusters organized as a hierarchical treeIntroduction to Data Mining 4/18/2004 7 Partitional ClusteringOriginal Points A Partitional ClusteringIntroduction to Data Mining 4/18/2004 8 Hierarchical Clusteringp4p1p3p2 p4 p1 p3 p2 p4p1 p2p3p4p1 p2p3Traditional Hierarchical ClusteringNon-traditional Hierarchical Clustering Non-traditional DendrogramTraditional DendrogramIntroduction to Data Mining 4/18/2004 9 Other Distinctions Between Sets of ClustersExclusive versus non-exclusive–In non-exclusive clusterings, points may belong to multiple clusters.–Can represent multiple classes or ‘border’ pointsFuzzy 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 characteristicsPartial versus complete–In some cases, we only want to cluster some of the dataHeterogeneous versus homogeneous–Cluster of widely different sizes, shapes, and densitiesIntroduction to Data Mining 4/18/2004 10 Types of Clusters Well-separated clusters Center-based clusters Contiguous clusters Density-based clustersProperty or ConceptualDescribed by an Objective FunctionIntroduction to Data Mining 4/18/2004 11 Types of Clusters: Well-SeparatedWell-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 clustersIntroduction to Data Mining 4/18/2004 12 Types of Clusters: Center-BasedCenter-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 clustersIntroduction to Data Mining 4/18/2004 13 Types of Clusters: Contiguity-BasedContiguous Cluster (Nearest neighbor or
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