Approximation Algorithms for K-Modes Clustering

TL;DR

This paper introduces a new approximation algorithm for k-modes clustering of categorical data, establishing its relation to k-median and extending metric-based algorithms, with empirical validation of its effectiveness.

Contribution

It connects k-modes to k-median, proves the metric property of k-modes, and develops a 2-approximation algorithm leveraging existing metric k-median methods.

Findings

The k-modes distance measure is a metric.

A deterministic 2-approximation algorithm for k-modes is proposed.

Empirical results show the method's superiority over existing approaches.

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 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.