Numerical optimization of a sum-of-rank-1 decomposition for n-dimensional order-p symmetric tensors

作者：Kyrgyzov Olexiy; Erdogmus Deniz

来源：Neurocomputing, 2010, 73(16-18): 3323-3327.

DOI：10.1016/j.neucom.2010.06.013

• Symmetric tensor decomposition
• Iterative optimization
• Basis vector frame

In this paper, we present a sum-of-rank-1 type decomposition and its differential model for symmetric tensors and investigate the convergence properties of numerical gradient-based iterative optimization algorithms to obtain this decomposition. The decomposition we propose reinterprets the orthogonality property of the eigenvectors of symmetric matrices as a geometric constraint on the rank-1 matrix bases, which leads to a geometrically constrained eigenvector frame. Relaxing the orthogonality requirement, we developed a set of structured-bases that can be utilized to decompose any symmetric tensor into a similar constrained sum-of-rank-1 decomposition.

• 出版日期2010-10
• 单位东北大学