Related papers: Low-rank multi-parametric covariance identificatio…

In this work we present Low-rank Deconvolution, a powerful framework for low-level feature-map learning for efficient signal representation with application to signal recovery. Its formulation in multi-linear algebra inherits properties…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and…

Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gr\"obner-basis or resultant-based methods due…

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a…

This paper addresses the challenge of classifying polarimetric SAR images by leveraging the peculiar characteristics of the polarimetric covariance matrix (PCM). To this end, a general framework to solve a multiple hypothesis test is…

Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…

The existing analysis of WMAP data is based on approximations for the likelihood function, which is likely to be inaccurate on large scales. Here we present exact evaluations of the likelihood of the low multipoles by direct inversion of…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

This paper investigates the problem of image segmentation using superpixels. We propose two approaches to enhance the discriminative ability of the superpixel's covariance descriptors. In the first one, we employ the Log-Euclidean distance…

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…

In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized…

Learning discriminative and invariant feature representation is the key to visual image categorization. In this article, we propose a novel invariant deep compressible covariance pooling (IDCCP) to solve nuisance variations in aerial scene…

We consider the problem of estimating missing values in trajectories of linear parameter-varying (LPV) systems. We solve this interpolation problem for the class of shifted-affine LPV systems. Conditions for the existence and uniqueness of…

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…

Low-rank regularization is an effective technique for addressing ill-posed inverse problems when the unknown variable exhibits low-rank characteristics. However, global low-rank assumptions do not always hold for seismic wavefields; in many…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…