Related papers: Low-Rank and Sparse Enhanced Tucker Decomposition …
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank theory. We call this property the max-full-rank-submatrix…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions…
A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…
In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…
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 novel factorization of…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Regular medical records are useful for medical practitioners to analyze and monitor patient health status especially for those with chronic disease, but such records are usually incomplete due to unpunctuality and absence of patients. In…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a…