Related papers: Subspace power method for symmetric tensor decompo…

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank,…

The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions…

Conjugate partial-symmetric (CPS) tensor is a generalization of Hermitian matrices. For the CPS tensor decomposition some properties are presented. For real CPS tensors in particular, we note the subtle difference from the complex case of…

We propose Selective Multiple Power Iterations (SMPI), a new algorithm to address the important Tensor PCA problem that consists in recovering a spike $\bf{v_0}^{\otimes k}$ corrupted by a Gaussian noise tensor $\bf{Z} \in…

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least…

This work is concerned with the computation of $\ell^p$-eigenvalues and eigenvectors of square tensors with $d$ modes. In the first part we propose two possible shifted variants of the popular (higher-order) power method %for the…

We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only…

In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…

We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…

The CANDECOMP/PARAFAC (or Canonical polyadic, CP) decomposition of tensors has numerous applications in various fields, such as chemometrics, signal processing, machine learning, etc. Tensor CP decomposition assumes the knowledge of the…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…

In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…

In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition. We establish the weak convergence, global convergence…

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-$1$ update which is the alternating version…

The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…