Related papers: Subset selection for matrices in spectral norm
Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
When, in terms of the number of data points, the size of a dataset exceeds available computing resources, or when labeling is expensive, an attractive solution consists of selecting only some of the data points (subdata) for further…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to select the modes relevant for reduction are usually…
Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…