Sequential subspace finding: A new algorithm for learning low-dimensional linear subspaces

In this paper we propose a new algorithm for learning low-dimensional linear subspaces. Our proposed algorithm performs by sequentially finding some low-dimensional subspaces on which a set of training data lies. Each subspace is found in such a way that the number of signals lying on (or near to) it is maximized. Once we found a subset of the training data that is sufficiently close to a subspace, then we omit these signals from the set of training signals and repeat the procedure for the remaining signals until all training signals are assigned to a subspace. This data reduction procedure results in a significant improvement to the runtime of our algorithm. We then propose a robust version of the algorithm to address the situation in which training signals are contaminated by additive white Gaussian noise. Our simulations on synthetic data and image denoising problem show the applicability and the promising performance of our algorithm.