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Approximation Algorithms for K-Modes Clustering

  • Zengyou He
  • Shengchun Deng
  • Xiaofei Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4114)

Abstract

In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and k-median, i.e., the optimum of k-median is at most the twice the optimum of k-modes for the same categorical data clustering problem. Based on this observation, we derive a deterministic algorithm that achieves an approximation factor of 2. Furthermore, we prove that the distance measure in k-modes defines a metric. Hence, we are able to extend existing approximation algorithms for metric k-median to k-modes. Empirical results verify the superiority of our method.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Zengyou He
    • 1
  • Shengchun Deng
    • 1
  • Xiaofei Xu
    • 1
  1. 1.Department of Computer Science and EngineeringHarbin Institute of TechnologyChina

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