Data clustering as an optimum-path forest problem ...
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Data Clustering as an Optimum-Path Forest Problem with Applications in Image Analysis Leonardo Marques Rocha,1 Fa´bio A. M. Cappabianco,2 Alexandre Xavier Falca˜o2 1
Department of Telecommunications, School of Electrical and Computer Engineering, University of Campinas, Brazil 2
Department of Information Systems, Institute of Computing, University of Campinas, Brazil
Received 6 August 2008; accepted 5 March 2009
ABSTRACT: We propose an approach for data clustering based on optimum-path forest. The samples are taken as nodes of a graph, whose arcs are defined by an adjacency relation. The nodes are weighted by their probability density values (pdf) and a connectivity function is maximized, such that each maximum of the pdf becomes root of an optimum-path tree (cluster), composed by samples ‘‘more strongly connected’’ to that maximum than to any other root. We discuss the advantages over other pdf-based approaches and present extensions to large datasets with results for interactive image segmentation and for fast, accurate, and automatic brain tissue classification in magnetic resonance (MR) images. We also include experimental C 2009 Wiley Periodicomparisons with other clustering approaches. V cals, Inc. Int J Imaging Syst Technol, 19, 50–68, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20191
I. INTRODUCTION The identification of natural groups of samples from a dataset, namely clustering (Duda et al., 2000) is a crucial step in many applications of data analysis. The samples are usually represented by feature vectors (e.g., points in
