Fast Randomized Matrix and Tensor Interpolative Decomposition Using CountSketch

TL;DR

A new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch and maintains the accuracy of competing methods, while running in less time, achieving at least an order of magnitude speedup on large matrices and tensors.

Abstract

We propose a new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch. We then extend this approach to the tensor interpolative decomposition problem introduced by Biagioni et al. (J. Comput. Phys. 281, pp. 116-134, 2015). Theoretical performance guarantees are provided for both the matrix and tensor settings. Numerical experiments on both synthetic and real data demonstrate that our algorithms maintain the accuracy of competing methods, while running in less time, achieving at least an order of magnitude speed-up on large matrices and tensors.