On GROUSE and incremental SVD

GROUSE (Grassmannian Rank-One Update Subspace Estimation) [1] is an incremental algorithm for identifying a subspace of ℝⁿ from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis [2] has shown that GROUSE converges locally at an expected linear rate, under certain assumptions. GROUSE has a similar flavor to the incremental singular value decomposition algorithm [4], which updates the SVD of a matrix following addition of a single column. In this paper, we modify the incremental SVD approach to handle missing data, and demonstrate that this modified approach is equivalent to GROUSE, for a certain choice of an algorithmic parameter.

I. Introduction

Subspace estimation and singular value decomposition have been important tools in linear algebra and data analysis for several decades. They are used to understand the principal components of a signal, to reject noise, and to identify best approximations.