Related papers: A fast algorithm for regularized focused 3-D inver…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…
This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD)…
In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a…
We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…
We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector…
Computing the top eigenvectors of a matrix is a problem of fundamental interest to various fields. While the majority of the literature has focused on analyzing the reconstruction error of low-rank matrices associated with the retrieved…
We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…
Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and…
The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This…
Classical data analysis requires computational efforts that become intractable in the age of Big Data. An essential task in time series analysis is the extraction of physically meaningful information from a noisy time series. One algorithm…
Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…
We study optimization of finite sums of geodesically smooth functions on Riemannian manifolds. Although variance reduction techniques for optimizing finite-sums have witnessed tremendous attention in the recent years, existing work is…
This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…
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…