Sparse Nonnegative Tensor Factorization and Completion With Noisy Observations

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial noisy observations for third-order tensors. Because of sparsity nonnegativity, underlying is decomposed into tensor-tensor product one tensor. We propose to minimize sum maximum likelihood estimation with nonnegativity constraints $\ell _{0}$ norm factor. show that error bounds estimator proposed model can be established under general noise observations. The detailed specific distributions including additive Gaussian noise, Laplace Poisson derived. Moreover, minimax lower are shown matched upper up a logarithmic factor sizes These theoretical results tensors better than those obtained matrices, illustrates advantage use models denoising. Numerical experiments provided validate superiority tensor-based method compared matrix-based approach.