An adaptive gradient method for computing generalized tensor eigenpairs

2016/01/07 by Gaohang Yu, Yu, Gaohang, Zefeng Yu +5
Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1601.01399

openalex publication_date 2016/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

High order tensor arises more and more often in signal processing,data analysis, higher-order statistics, as well as imaging sciences. In this paper, an adaptive gradient (AG) method is presented for generalized tensor eigenpairs. Global convergence and linear convergence rate are established under some suitable conditions. Numerical results are reported to illustrate the efficiency of the proposed method. Comparing with the GEAP method, an adaptive shifted power method proposed by Tamara G. Kolda and Jackson R. Mayo [SIAM J. Matrix Anal. Appl., 35 (2014), pp. 1563-1581], the AG method is much faster and could reach the largest eigenpair with a higher probability.

Citations

• Most Tensor Problems Are NP-Hard

Related

• Tensor-based Dinkelbach method for computing generalized tensor eigenvalues and its applications
• Accelerating the Computation of Tensor Z-eigenvalues
• Spectral projected gradient methods for generalized tensor eigenvalue complementarity problem
• Computing tensor eigenvalues via homotopy methods
• An adaptive cubic regularization method for computing extreme eigenvalues of tensors