Learning low-dimensional subspaces via sequential subspace fitting

Abstract

In this paper we address the problem of learning low-dimensional subspaces using a given set of training data. To this aim, we propose an algorithm that performs by sequentially fitting a number of low-dimensional subspaces to the training data. Once we found a subset of the training data that is sufficiently near a fitted subspace, we omit these signals from the set of training signals and repeat the same procedure for the remaining signals until all training signals are assigned to a subspace. We then propose a robust version of the algorithm to address the situation in which the training signals are contaminated by additive white Gaussian noise (AWGN). Experimental results on both synthetic and real data show the promising performance of our proposed algorithm.