Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method

2016/07/25 by Tsung-Lin Lee, Lee, Tsung-Lin, Yueh‐Cheng Kuo +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1607.07128

openalex publication_date 2016/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only depends on the dimension of the tensor and the proof is constructive. Under these conditions, an algorithm applying homotopy continuation method is developed for computing the CP decomposition of tensors.

Citations

• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

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