External validation measures for K-means clustering: A data distribution perspective

  • Authors:
  • Junjie Wu;Jian Chen;Hui Xiong;Ming Xie

  • Affiliations:
  • School of Economics and Management, Beihang University, Beijing 100083, China;Research Center for Contemporary Management, Key Research Institute of Humanities and Social Sciences at Universities, Tsinghua University, Beijing 100084, China;Management Science and Information Systems Department, Rutgers University, Newark 07102, NJ, USA;Research Center for Contemporary Management, Key Research Institute of Humanities and Social Sciences at Universities, Tsinghua University, Beijing 100084, China

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2009

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Abstract

Cluster validation is an important part of any cluster analysis. External measures such as entropy, purity and mutual information are often used to evaluate K-means clustering. However, whether these measures are indeed suitable for K-means clustering remains unknown. Along this line, in this paper, we show that a data distribution view is of great use to selecting the right measures for K-means clustering. Specifically, we first introduce the data distribution view of K-means, and the resultant uniform effect on highly imbalanced data sets. Eight external measures widely used in recent data mining tasks are also collected as candidates for K-means evaluation. Then, we demonstrate that only three measures, namely the variation of information (VI), the van Dongen criterion (VD) and the Mirkin metric (M), can detect the negative uniform effect of K-means in the clustering results. We also provide new normalization schemes for these three measures, i.e., VI"n"o"r"m^', VD"n"o"r"m^' and M"n"o"r"m^', which enables the cross-data comparisons of clustering qualities. Finally, we explore some properties such as the consistency and sensitivity of the three measures, and give some advice on how to use them in K-means practice.