Related papers: Semi-parametric TEnsor Factor Analysis by Iterativ…

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

The Singular Value Decomposition (SVD) of matrices is a widely used tool in scientific computing. In many applications of machine learning, data analysis, signal and image processing, the large datasets are structured into tensors, for…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the…

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 higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms…

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general 4-order tensor model that enables computationally…

In this paper, we introduce a novel method of neural network weight compression. In our method, we store weight tensors as sparse, quantized matrix factors, whose product is computed on the fly during inference to generate the target…

Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…

We propose a new matrix factor model, named RaDFaM, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. RaDFaM contributes a novel class…