The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor

2021/11/05 by Amina Sabir, Sabir, Amina, Pegnfei Huang +3
Mathematics · #15A69 #15B57 #41A50 #90C26 #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2111.03238

openalex publication_date 2021/11/05 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric (CPS) tensor and show that the greedy successive rank-one approximation (SROA) algorithm can recover this decomposition exactly. Based on this matrix decomposition, the CP rank of CPS tensor can be bounded by the matrix rank, which can be applied to low rank tensor completion. Additionally, we give the rank-one equivalence property for the CPS tensor based on the SVD of matrix, which can be applied on the rank-one approximation for CPS tensors.

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