An Experimental Evaluation of a Monte-Carlo Algorithm for Singular Value Decomposition

We demonstrate that an algorithm proposed by Drineas et. al. in [7] to approximate the singular vectors/values of a matrix A, is not only of theoretical interest but also a fast, viable alternative to traditional algorithms. The algorithm samples a small number of rows (or columns) of the matrix, scales them appropriately to form a small matrix S and computes the singular value decomposition (SVD) of S, which is a good approximation to the SVD of the original matrix. We experimentally evaluate the accuracy and speed of this randomized algorithm using image matrices and three different sampling schemes. Our results show that our approximations of the singular vectors of A span almost the same space as the corresponding exact singular vectors of A.

• Type: Conference
• Year: 2001
• Where: PCI
• Authors: Petros Drineas, Eleni Drinea, Patrick S. Huggins
• Keywords: Informatics, PCI 2001, Singular Value Decomposition, Singular Vectors, Singular Vectors/values