Sparse Nonnegative Tensor Factorization and Completion with Noisy Observations
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the tensor-tensor product of one sparse nonnegative tensor and one nonnegative tensor. We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor $\ell_0$ norm for the sparse factor. We show that the error bounds of the estimator of the proposed model can be established under general noise observations. The detailed error bounds under specific noise distributions including additive Gaussian noise, additive Laplace noise, and Poisson observations can be derived. Moreover, the minimax lower bounds are shown to be matched with the established upper bounds up to a logarithmic factor of the sizes of the underlying tensor. These theoretical results for tensors are better than those obtained for matrices, and this illustrates the advantage of the use of nonnegative sparse tensor models for completion and denoising. Numerical experiments are provided to validate the superiority of the proposed tensor-based method compared with the matrix-based approach.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingSimilar Papers 제목 키워드 기반
Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion
Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a no…
Image InpaintingNoisy Nonnegative Tucker Decomposition with Sparse Factors and Missing Data
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, ma…
Tensor DecompositionEfficient Nonnegative Tensor Factorization via Saturating Coordinate Descent
With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer use…
Accelerated Stochastic Gradient for Nonnegative Tensor Completion and Parallel Implementation
We consider the problem of nonnegative tensor completion. We adopt the alternating optimization framework and solve each nonnegative matrix completion problem via a stochastic variation of the accelerated gradient algori…
Matrix CompletionSWIFT: Scalable Wasserstein Factorization for Sparse Nonnegative Tensors
Existing tensor factorization methods assume that the input tensor follows some specific distribution (i.e. Poisson, Bernoulli, and Gaussian), and solve the factorization by minimizing some empirical loss functions defin…
Computational Efficiency