Shifted Randomized Singular Value Decomposition

Ali Basirat

Keywords: SVD, PCA, Randomized Algorithms

TL;DR: A randomized algorithm to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory.

Abstract: We extend the randomized singular value decomposition (SVD) algorithm (Halko et al., 2011) 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.

Code: https://drive.google.com/file/d/1bjG5kAQ9WoTbQKFX41SnHW9eaik_SujD/view?usp=sharing