Block Randomized Singular Value Decomposition on GPUs

Abstract

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. For processing large-scale data, computing systems with accelerators like GPUs have become the mainstream approach. In those systems, access to the input data dominates the overall process time; therefore, it is needed to design an out-of-core algorithm to dispatch the computation into accelerators. This paper proposes an accurate two-pass randomized SVD, named block randomized SVD (BRSVD), designed for matrices with a slow-decay singular spectrum that is often observed in image data. BRSVD fully utilizes the power of modern computing system architectures and efficiently processes large-scale data in a parallel and out-of-core fashion. Our experiments show that BRSVD effectively moves the performance bottleneck from data transfer to computation, so that outperforms existing randomized SVD methods in terms of speed with retaining similar accuracy.

Background Subtraction using Adaptive Singular Value Decomposition

“…This factorization is rank revealing and can be efficiently calculated via random sampling. To further speed up the randomized approaches, which tend to have good parallelization abilities, Lu et al offer a way to blockwisely move parts of the calculations onto the GPU in [19]. For our application, however, it is important that the low-rank subspace calculation algorithm is extendable to an iteratively growing data matrix which is not available in the aforementioned fast SVD calculation approaches.…”