An unsupervised data projection that preserves the cluster structure

In this paper we propose a new unsupervised dimensionality reduction algorithm that looks for a projection that optimally preserves the clustering data structure of the original space. Formally we attempt to find a projection that maximizes the mutual information between data points and clusters in the projected space. In order to compute the mutual information, we neither assume the data are given in terms of distributions nor impose any parametric model on the within-cluster distribution. Instead, we utilize a non-parametric estimation of the average cluster entropies and search for a linear projection and a clustering that maximizes the estimated mutual information between the projected data points and the clusters. The improved performance is demonstrated on both synthetic and real world examples.