Rayleigh-Ritz Based Updates of the Multilinear Singular Value Decomposition

Multilinear singular value decomposition (MLSVD), also known as Higher-order SVD (HOSVD), is a popular method for approximating a tensor of order ≥ 3 via a smaller core tensor and corresponding factor matrices. While MLSVD has found numerous applications, it is not designed to handle tensors that vary over time. In this work we propose an algorithm for updating the MLSVD of an evolving tensor via leveraging Rayleigh-Ritz matrix projection techniques. In particular, we consider the case where at each time step the dimensions of the tensor are augmented and its entries may change. Preliminary tests on synthetic and real data showcase the potential of the proposed approach.