IncTSVD: Incremental Tensor Singular Value Decomposition of Multidimensional Streaming Data.

Abstract

In this article, we develop an online method called IncTSVD to incrementally compute the tensor singular value decomposition (TSVD) of a given sequence of third-order tensors based on the tensor-tensor concept. This can be considered an extension of incremental SVD based on updating matrices to tensors. IncTSVD is suitable for streamed tensor data and where memory resources are limited. Most existing methods to compute TSVD focus on approximating it using randomized or sketching techniques in a batch setting to decrease the storage and computational costs required. The IncTSVD extends the computation of TSVD to streaming by maintaining the basis tensors of previously arrived data and incrementally updating the approximation using the tensor of incoming data. The computational cost and approximation error of the proposed method were analyzed theoretically and through extensive numerical experiments, which included using synthetic and real-world datasets under streaming scenarios. The IncTSVD method was superior to existing deterministic and randomized tensor decompositions (TDs) based on the t-product for computational and storage costs, and had comparable accuracy to the standard TSVD method.