Orthogonal random projection for tensor completion

Abstract

The low‐rank tensor completion problem, which aims to recover the missing data from partially observable data. However, most of the existing tensor completion algorithms based on Tucker decomposition cannot avoid using singular value decomposition (SVD) operation to calculate the Tucker factors, so they are not suitable for the completion of large‐scale data. To solve this problem, they propose a new faster tensor completion algorithm, which uses the method of random projection to project the unfolding matrix of each mode of the tensor into the low‐dimensional subspace, and then obtain the Tucker factors by the orthogonal decomposition. Their method can effectively avoid the high computational cost of SVD operation. The results of the synthetic data experiments and real data experiments verify the effectiveness and feasibility of their method.

Keywords

• orthogonal random projection
• low-rank tensor completion problem
• missing data
• partially observable data
• Tucker decomposition
• singular value decomposition operation