A Novel Tensor Tracking Algorithm for Block-Term Decomposition of Streaming Tensors

Block-term decomposition (BTD), which factorizes a tensor (aka a multiway array) into block components of low rank, has been a powerful processing tool for multivariate and high-dimensional data analysis. In this paper, we propose a novel tensor tracking method called SBTD for factorizing tensors derived from multidimensional data streams under the BTD format. Thanks to the alternating optimization framework, SBTD first applies a regularized least-squares solver to estimate the temporal factor of the underlying streaming tensor. Then, SBTD adopts an adaptive filter to track the non-temporal tensor factors over time by minimizing a weighted least-squares cost function. Numerical experiments indicate that SBTD is capable of tensor tracking with competitive performance compared to the state-of-the-art BTD algorithms.