A Randomized Algorithm for Approximating Truncated SVD

Abstract

Matrices with low-rank structure are frequently encountered in a myriad of application domains, due to Big Data generation and consumption. Low-rank matrix decomposition algorithms, such as the truncated singular value decomposition (TSVD), play a pivotal role in processing and extracting patterns of such data matrices. We present in this work an algorithm termed Randomized Rank-k QLP (RR-QLP). It utilizes randomization and efficiently constructs a low-rank decomposition of an input matrix, thus providing an approximation to the TSVD. Its advantage over TSVD, however, is that RR-QLP is computationally more efficient and can leverage the parallel structure of modern computers, thereby tackling a major bottle- neck associated with TSVD. To show the effectiveness of RR-QLP, different classes of data matrices are treated and the results are compared with those of several algorithms from the literature.