Unsupervised dictionary learning with Fisher discriminant for clustering

Abstract

In this paper, we propose a novel Fisher discriminant unsupervised dictionary learning (FD-UDL) approach, for improving the clustering performance of state-of-the-art dictionary learning approaches in unsupervised scenarios. This is achieved by employing a novel Fisher discriminant criterion on dictionary elements to encourage the diversity between different sub-dictionaries, and also the coherence within each sub-dictionary. Such a discriminant is incorporated to formulate the optimization problem of unsupervised dictionary learning. Furthermore, we provide an analytical solution to the proposed optimization problem, obtaining the learned dictionary for clustering tasks. Unlike previous approaches for unsupervised clustering, the proposed FD-UDL approach takes into account both within-class and between-class scatters of sub-dictionaries, rather than only considering diversity between different sub-dictionaries. Finally, experiments on synthetic data, face and handwritten digit clustering tasks show the improved clustering accuracy over other state-of-the-art dictionary learning and clustering approaches.