Title: Randomized algorithms for low-rank tensor decompositions
Abstract: Many applications in data science and scientific computing require the working with large-scale datasets that are expensive to store and manipulate. These datasets have inherent multidimensional structure that can be exploited in order to efficiently compress and store them in an appropriate tensor format. In recent years, randomized matrix methods have been used to efficiently and accurately compute low-rank matrix decompositions. Motivated by this success, we develop several randomized algorithms for compressing tensor datasets in the Tucker format. We present probabilistic error analysis for our algorithms and numerical results on several datasets: synthetic test tensors, and realistic applications including the compression of facial image samples in the Olivetti database, and word counts in the Enron email dataset.
Joint work with Rachel Minster (NC State) and Misha Kilmer (Tufts)