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.
CITATION STYLE
He, Z., Deng, S., & Xu, X. (2006). Approximation Algorithms for K-Modes Clustering (pp. 296–302). https://doi.org/10.1007/978-3-540-37275-2_38
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