On GROUSE and Incremental SVD
This work provides an incremental method for subspace estimation with missing data, which is incremental as it builds on existing algorithms like GROUSE and incremental SVD.
The paper tackles the problem of subspace identification from incomplete data by modifying the incremental SVD algorithm to handle missing data, showing that this modification is equivalent to the GROUSE algorithm under specific parameter settings.
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.