Related papers: General Tensor Decomposition, Moment Matrices and …
Truncated singular value decomposition is a reduced version of the singular value decomposition in which only a few largest singular values are retained. This paper presents a novel perturbation analysis for the truncated singular value…
We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
We are concerned with the eigenstructure of supersymmetric tensors. Like in the matrix case, normalized tensor eigenvectors are fixed points of the tensor power iteration map. However, unless the given tensor is orthogonally decomposable,…
We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A.V. Shtraus on the generalized resolvents of symmetric operators. All…
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$, over a fixed finite field can be done in polynomial time. However, if some cells in the tensor are allowed to have arbitrary values, then rank-2 is NP-hard over the…