On the Relationship Between Dimensionality Reduction and Spectral Clustering from a Kernel Viewpoint

Abstract

This paper presents the development of a unified view of spectral clustering and unsupervised dimensionality reduction approaches within a generalized kernel framework. To do so, the authors propose a multipurpose latent variable model in terms of a high-dimensional representation of the input data matrix, which is incorporated into a least-squares support vector machine to yield a generalized optimization problem. After solving it via a primal-dual procedure, the final model results in a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Specifically, our formulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.