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.
翻译:我们为四阶对称部分对称(CPS)电压,提出了一个正方位矩阵外产分解法,并表明贪婪的连续一级近似(SROA)算法可以完全恢复这一分解。根据这一矩阵分解法,CPS 高方位的CP等级可以受可适用于低级高分补的矩阵等级的约束。此外,我们根据SVD矩阵为CPS 电压(SVD)提供CPS 等价财产,该等价财产可以适用于CPS 高压的一级近似值。