Shifted Randomized Singular Value Decomposition

TL;DR

This paper introduces an extension to the randomized SVD algorithm that efficiently computes the SVD of shifted data matrices without explicit matrix construction, improving low-rank approximation and PCA for off-center data.

Contribution

The paper presents a novel extension to randomized SVD that handles shifted matrices efficiently, maintaining accuracy and enabling better PCA on off-center data.

Findings

Enhanced efficiency in matrix factorization for shifted matrices

Maintains accuracy of the original randomized SVD

Demonstrated advantages on various data matrices

Abstract

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the original algorithm, the extended algorithm provides for a more efficient way of matrix factorization. The algorithm facilitates the low-rank approximation and principal component analysis (PCA) of off-center data matrices. When applied to different types of data matrices, our experimental results confirm the advantages of the extensions made to the original algorithm.