6 research outputs found
A Randomized Algorithm for Tensor Singular Value Decomposition using an Arbitrary Number of Passes
Efficient and fast computation of a tensor singular value decomposition
(t-SVD) with a few passes over the underlying data tensor is crucial because of
its many potential applications. The current/existing subspace randomized
algorithms need (2q+2) passes over the data tensor to compute a t-SVD, where q
is a non-negative integer number (power iteration parameter). In this paper, we
propose an efficient and flexible randomized algorithm that can handle any
number of passes q, which not necessary need be even. The flexibility of the
proposed algorithm in using fewer passes naturally leads to lower computational
and communication costs. This advantage makes it particularly appropriate when
our task calls for several tensor decompositions or when the data tensors are
huge. The proposed algorithm is a generalization of the methods developed for
matrices to tensors. The expected/ average error bound of the proposed
algorithm is derived. Extensive numerical experiments on random and real-world
data sets are conducted, and the proposed algorithm is compared with some
baseline algorithms. The extensive computer simulation experiments demonstrate
that the proposed algorithm is practical, efficient, and in general outperforms
the state of the arts algorithms. We also demonstrate how to use the proposed
method to develop a fast algorithm for the tensor completion problem