A super-resolution framework for tensor decomposition. (6th April 2022)

• Record Type: Journal Article
• Authors: Li, Qiuwei; Prater, Ashley; Shen, Lixin; Tang, Gongguo
• Is Part Of: Information and inference. Volume 11:Number 4(2022)
• Page Start: 1287
• Page End: 1328
• Publication Date: 2022-04-06
• Subjects: atomic norm minimization -- dual certificate -- nonconvex -- tensor decomposition -- tensor nuclear norm -- super resolution; Mathematical models -- Periodicals; 519.605
• DOI: 10.1093/imaiai/iaac002
• Languages: English
• ISSNs: 2049-8764

Abstract

Abstract: This work considers a super-resolution framework forovercomplete tensor decomposition. Specifically, we view tensor decomposition as a super-resolution problem of recovering a sum of Dirac measures on the sphere and solve it by minimizing a continuous analog of the $\ell _1$ norm on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Similar to the separation condition in the super-resolution problem, by explicitly constructing a dual certificate, we develop incoherence conditions of the tensor factors so that they form the unique optimal solution of the continuous analog of $\ell _1$ norm minimization. Remarkably, the derived incoherence conditions are satisfied with high probability by random tensor factors uniformly distributed on the sphere, implying global identifiability of random tensor factors.