# Guaranteed Functional Tensor Singular Value Decomposition

arXiv: https://arxiv.org/abs/2108.04201 · HTML: https://mlsanity.com/paper/2108.04201/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2021.

## Built on by (most cited first, 10 of 10)

- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data](https://mlsanity.com/paper/2408.05677/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)
- [Integrated Analysis for Electronic Health Records with Structured and Sporadic Missingness](https://mlsanity.com/paper/2506.09208/) (2025)
- [Adaptive Subspace Modeling With Functional Tucker Decomposition](https://mlsanity.com/paper/2603.25530/) (2026)
- [Low-rank Distributional Matrix Completion](https://mlsanity.com/paper/2606.04176/) (2026)
- [Low-Rank and Structured Sparse Tensor Decomposition for Anomaly Detection in Multivariate Functional Data](https://mlsanity.com/paper/2610.06930/) (2026)

## Abstract (arXiv)

This paper 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.