Guaranteed Functional Tensor Singular Value Decomposition

This article introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one mode and several tabular modes. The problem is motivated by high-order longitudinal data analysis. Our model assumes observed to be random realization of an approximate CP low-rank measured on discrete time grid. Incorporating algebra theory reproducing kernel Hilbert space (RKHS), we propose RKHS-based constrained power iteration spectral initialization. method can successfully estimate both vectors functions structure in data. With mild assumptions, establish non-asymptotic contractive error bounds proposed algorithm. superiority demonstrated via extensive experiments simulated real Supplementary materials this are available online.