Related papers: A Block-Randomized Stochastic Method with Importan…
Random projections reduce the dimension of a set of vectors while preserving structural information, such as distances between vectors in the set. This paper proposes a novel use of row-product random matrices in random projection, where we…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
The matricized-tensor times Khatri-Rao product computation is the typical bottleneck in algorithms for computing a CP decomposition of a tensor. In order to develop high performance sequential and parallel algorithms, we establish…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the…
A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast…
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…
In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…
We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on…
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale…
Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…