Optimal Scoring for Unsupervised Learning

We are often interested in casting classification and clustering problems as a regression framework, because it is feasible to achieve some statistical properties in this framework by imposing some penalty criteria. In this paper we illustrate optimal scoring, which was originally proposed for performing the Fisher linear discriminant analysis by regression, in the application of unsupervised learning. In particular, we devise a novel clustering algorithm that we call optimal discriminant clustering. We associate our algorithm with the existing unsupervised learning algorithms such as spectral clustering, discriminative clustering and sparse principal component analysis. Experimental results on a collection of benchmark datasets validate the effectiveness of the optimal discriminant clustering algorithm.