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Bregman Bubble Clustering A Robust Scalable Framework for Locating Multiple Dense Regions in Data Gunjan Gupta Joydeep Ghosh Department of Electrical Computer Engineering University of Texas at Austin Austin TX 78712 USA ggupta ghosh ece utexas edu Abstract In traditional clustering every data point is assigned to at least one cluster On the other extreme One Class Clustering algorithms proposed recently identify a single dense cluster and consider the rest of the data as irrelevant However in many problems the relevant data forms multiple natural clusters In this paper we introduce the notion of Bregman bubbles and propose Bregman Bubble Clustering BBC that seeks k dense Bregman bubbles in the data We also present a corresponding generative model Soft BBC and show several connections with Bregman Clustering and with a One Class Clustering algorithm Empirical results on various datasets show the effectiveness of our method 1 Introduction Many unsupervised learning problems involve summarizing the data using a small number of parameters Algorithms such as K Means partition the data into k clusters directly for a given k while other methods give a hierarchy of clusters However in many real world problems only a subset can be summarized well while the rest of the data shows little or no clustering tendencies Typically in such cases only a portion of the data containing multiple natural groupings is relevant These include 1 Market basket data where only a subset of customers show coherent behavior 2 Many web mining applications where recovering the most relevant items of key categories is more important than obtaining an exhaustive list 3 Many types of bioinformatics datasets For example gene expression datasets measure expression level of genes compared to a control across a few thousand genes The experiments typically cover only a specific theme such as stress response and therefore only a few genes related to the conditions show good clustering Biologists are

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