Approximation Algorithms for K-Modes Clustering

Details Approximation Algorithms for K-Modes Clustering Approximation Algorithms for K-Modes Clustering

2006-03-30

arxiv.org/abs/cs/0603120v1

Computer Science

Artificial Intelligence

7 pages

Scientific paper

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 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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