Guaranteed Functional Tensor Singular Value Decomposition

Rungang Han, Pixu Shi and Anru R. Zhang

Journal of the American Statistical Association, 2024, vol. 119, issue 546, 995-1007

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

Date: 2024
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DOI: 10.1080/01621459.2022.2153689

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