Tensor completion via functional smooth component deflation

Abstract

For the matrix/tensor completion problem with very high missing ratio, the standard local (e.g., patch, probabilistic, and smoothness) and global (e.g., low-rank) structure-based methods do not work well. To address this issue, we proposed to use local and global data structures at the same time by applying a novel functional smooth PARAFAC decomposition model for the tensor completion. This decomposition model is constructed as a sum of the outer product of functional smooth component vectors, which are represented by linear combinations of smooth basis functions. A new algorithm was developed by applying greedy deflation and smooth rank-one tensor decomposition. Our extensive experiments demonstrated the high performance and advantages of our algorithm in comparison to existing state-of-the-art methods.