The performance of objective functions for clustering categorical data

Partitioning methods, such as k-means, are popular and useful for clustering. Recently we proposed a new partitioning method for clustering categorical data: using the transfer algorithm to optimize an objective function called within-cluster dispersion. Preliminary experimental results showed that this method outperforms a standard method called k-modes, in terms of the average quality of clustering results. In this paper, we make more advanced efforts to compare the performance of objective functions for categorical data. First we analytically compare the quality of three objective functions: k-medoids, k-modes and within-cluster dispersion. Secondly we measure how well these objectives find true structures in real data sets, by finding their global optima, which we argue is a better measurement than average clustering results. The conclusion is that within-cluster dispersion is generally a better objective for discovering cluster structures. Moreover, we evaluate the performance of various distance measures on within-cluster dispersion, and give some useful observations.