Fast Eigen Decomposition for Low-Rank Matrix Approximation
Provides a novel method for eigen decomposition in low-rank matrix approximation, addressing a limitation of SVD for practitioners dealing with signed weights.
The paper presents an efficient algorithm for eigen decomposition of matrices formed as weighted sums of outer products, handling both positive and negative weights, unlike SVD which requires nonnegative weights.
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen decomposition of such matrices is though the singular value decomposition, which is available only if all the weights are nonnegative. Our proposed algorithm accepts both positive and negative weights.