Jay AndersonJay Anderson (continued)CUREAgendaWhat is Clustering?Traditional AlgorithmsThe All-Points ApproachThe All-Points ExampleThe Centroid ApproachThe Centroid ExampleDisadvantagesCURECURE (continued)CURE (Continued)Q+AJay Anderson•4.5th Year Senior•Major: Computer Science•Minor: Pre-Law•Interests: GT Rugby, Claymore, Hip Hop, Trance, Drum and Bass, Snowboarding etc.Jay Anderson (continued)CUREAn Efficient Clustering Algorithm for Large DatabasesSudipto Guha Rajeev Rastogi Kyuseok Shimpresented by Jay AndersonAgenda•What is clustering?•Traditional Algorithms–Centroid Approach–All-Points Approach•CURE•Conclusion•Q&AWhat is Clustering?•Clustering is the classification of objects into different groups.•Clustering algorithms are typically hierarchical–Think iterative, divide and conquer•or partitional–Think function optimizationTraditional AlgorithmsAll-Points Baseddmin, dmaxCentroid Baseddavg, dmeanThe All-Points ApproachAny point in the cluster is representative of the cluster.dmin(Ca, Cb) = minimum( || pa,i – pb,j || )dmax(Ca, Cb) = maximum( || pa,i – pb,j || )dmin represents the minimum distance between two points of a pair of clusters. It’s counterpart, dmax works similarly for divisive algorithms in that the pair of points furthest away from each determines who gets voted off the island.The All-Points ExampleAny point in the cluster is representative of the cluster.The Centroid ApproachClusters as represented by a single point.dmean(Ca, Cb) = || ma – mb ||davg(Ca, Cb) = (1/na*nb) * Σ[a] Σ[b] || pa – pb || These distance formulas find a centroid for each cluster. In identifying a central point, these algorithms prevent the ‘chaining’ by effectively creating a radius for possible clustering from the chosen point.The Centroid ExampleClusters as represented by a single point.Disadvantages•Hierarchical models are typically fast and efficient. As a result they are also popular. However there are some disadvantages.•Traditional clustering algorithms favor clusters approximating spherical shapes, similar sizes and are poor at handling outliers.CURE•Attempts to eliminate the disadvantages of the centroid approach and all-points approaches by presenting a hybrid of the two.•1) Identifies a set of well scattered points, representative of a potential cluster’s shape.•2) Scales/shrinks the set by a factor α to form (semi-centroids).•3) Merges semi-centroids at each iterationCURE(continued)Shrinking the sets, increases the distance from each cluster to any outlier, possibly the distance beyond the threshold and, mitigating the ‘chaining’ effect.Choosing well ‘scattered points’ representative of the cluster’s shape allows more precision than a standard spheroid radius.αCURE(Continued)•Time Complexity: O(n2 log n)–O(n2) for low dimensionality•Space Complexity O(n)–Heap and tree structures require linear
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