A review on the selection criteria for the truncated SVD in Data Science applications

Abstract

The Singular Value Decomposition (SVD) is one of the most used factorizations when it comes to Data Science applications. In particular, given the big size of the processed matrices, in most of the cases, a truncated SVD algorithm is employed. In the following manuscript, we review some of the state-of-the-art approaches considered for the selection of the number of components (i.e., singular values) to retain to apply the truncated SVD. Moreover, three new approaches based on the Kullback–Leibler divergence and on unsupervised anomaly detection algorithms, are introduced. The revised methods are then compared on some standard benchmarks in the image processing context.