Nonnegative low multi‐rank third‐order tensor approximation via transformation

Author:

Song Guang‐Jing1,Hu Yexun2,Xu Cobi3,Ng Michael K.4

Affiliation:

1. School of Mathematics and Information Sciences Weifang University Weifang People's Republic of China

2. School of Computing and Artificial Intelligence Southwestern University of Finance and Economics Chengdu People's Republic of China

3. Department of Mathematics The University of Hong Kong Pokfulam Hong Kong

4. Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

Abstract

AbstractThe main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions.

Funder

National Natural Science Foundation of China

Publisher

Wiley

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