Zhen-Wai Olivier Ho

Stephane Chretien, Zhen-Wai Olivier Ho

A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analysis. In this paper, we propose a perturbation bound for the smallest singular value of a given matrix after appending a column, under the assumption that its initial coherence is not large, and we use this bound to derive a fast algorithm for feature extraction.

Stephane Chretien, Christophe Guyeux, Zhen-Wai Olivier HO

This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvements can be achieved by learning the learning rate.