Approximation Algorithms for K-Modes Clustering
  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.
