A New Model for Tensor Completion: Smooth Convolutional Tensor Factorization

Abstract

Tensor completion is the problem of filling-in missing parts of multidimensional data using the values of the reference elements. Recently, Multiway Delay-embedding Transform (MDT), which considers a low-dimensional space in a delay-embedded space with high expressive capability, has attracted attention as a tensor completion method. Although MDT has a high complementary performance, its computational cost is considerably high. Therefore, we propose a new model called smooth convolutional tensor factorization (SCTF) for tensor completion based on a delay-embedded space. The proposed method is small in computational complexity because of its concise model of rank-1 decomposition in the delay-embedded space, and because it does not directly perform optimization in the delay-embedded space. In addition, a smooth constraint term is assigned to the factor tensors as a prior data structure in the optimization to improve the completion accuracy further. In our experiments, we completed clipped and random missing image data, and confirmed that the proposed method achieved high completion accuracy without high computational cost.

Keywords

• Tensor completion
• convolution
• tensor factorization
• delay-embedded space