On GROUSE and Incremental SVD

TL;DR

This paper demonstrates that a modified incremental SVD algorithm for handling missing data is equivalent to the GROUSE algorithm, providing insights into their relationship and convergence properties.

Contribution

It establishes the equivalence between a modified incremental SVD method and GROUSE for subspace estimation with missing data.

Findings

Modified incremental SVD handles missing data effectively.

Equivalence between modified SVD and GROUSE is proven.

Convergence properties are analyzed under certain assumptions.

Abstract

GROUSE (Grassmannian Rank-One Update Subspace Estimation) 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 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, 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.