Efficient and Learnable Transformed Tensor Nuclear Norm with Exact Recoverable Theory

Jiangjun Peng, Hailin Wang, Xiangyong Cao, Hongying Zhang, Xixi Jia, Deyu Meng

Keywords: Efficient, Learnable Transformed Tensor Nuclear Norm, Exact Recoverable Theory

TL;DR: This article first presents an efficient learnable transformed tensor nuclear norm (TNN) model with a recoverable theoretical guarantee.

Abstract:

The tensor nuclear norm represents the low-rank property of tensor slices under a transformation. Finding a good transformation is crucial for the tensor nuclear norm. However, existing transformations are either fixed and not adaptable to the data, leading to ineffective results, or they are nonlinear and non-invertible, which prevents theoretical guarantees for the transformed tensor nuclear norm. Besides, some transformations are too complex and computationally expensive. To address these issues, this paper first proposes a fast data-adaptive and learnable column-orthogonal transformation learning framework with an exact recoverable theoretical guarantee. Extensive experiments have validated the effectiveness of the proposed models and theories.

Submission Number: 30