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This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an $n \times q$ matrix, $\X^* =[ \x_1^*, \x_2^*, \cdots , \x_q^*]$ from $m$ independent linear projections of each…

Image and Video Processing · Electrical Eng. & Systems 2023-11-08 Silpa Babu , Namrata Vaswani

In this paper we introduce a new column selection strategy, named here ``Deviation Maximization", and apply it to compute rank-revealing QR factorizations as an alternative to the well known block version of the QR factorization with the…

Numerical Analysis · Mathematics 2022-06-03 Monica Dessole , Fabio Marcuzzi

In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…

Computer Vision and Pattern Recognition · Computer Science 2013-02-06 Ehsan Elhamifar , Rene Vidal

We suggest an efficient algorithm for the selection of sparse subsets of a set of influence for the numerical discretization of differential operators on irregular nodes with polynomial consistency of a given order with the help of the QR…

Numerical Analysis · Mathematics 2019-08-06 Oleg Davydov

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

Machine Learning · Computer Science 2021-09-20 Ruslan Khalitov , Tong Yu , Lei Cheng , Zhirong Yang

Unsupervised feature selection has been always attracting research attention in the communities of machine learning and data mining for decades. In this paper, we propose an unsupervised feature selection method seeking a feature…

Machine Learning · Computer Science 2015-06-04 Sen Wang , Feiping Nie , Xiaojun Chang , Lina Yao , Xue Li , Quan Z. Sheng

The classic rank-revealing QR factorization factorizes a matrix $A$ as $AP=QR$ where $P$ permutes the columns of $A$, $Q$ is an orthogonal matrix, and $R$ is upper triangular with non-increasing diagonal entries. This is called…

Numerical Analysis · Mathematics 2019-05-27 Reid Atcheson

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

Data Structures and Algorithms · Computer Science 2020-07-15 David P. Woodruff , Amir Zandieh

We advocate a numerically reliable and accurate approach for practical parameter identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead of computing an eigenvalue decomposition of the Fischer…

Numerical Analysis · Mathematics 2022-05-10 Katherine J. Pearce , Ilse C. F. Ipsen , Mansoor A. Haider , Arvind K. Saibaba , Ralph C. Smith

Feature selection aims to identify the most pattern-discriminative feature subset. In prior literature, filter (e.g., backward elimination) and embedded (e.g., Lasso) methods have hyperparameters (e.g., top-K, score thresholding) and tie to…

Machine Learning · Computer Science 2024-03-07 Wangyang Ying , Dongjie Wang , Haifeng Chen , Yanjie Fu

We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…

Machine Learning · Computer Science 2016-02-09 Weiran Wang

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…

Machine Learning · Statistics 2023-08-02 Junxian Zhu , Jin Zhu , Borui Tang , Xuanyu Chen , Hongmei Lin , Xueqin Wang

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important…

Machine Learning · Computer Science 2022-01-24 Jeremy E. Cohen

An algorithm is provided for performing polynomial feature expansions that both operates on and produces compressed sparse row (CSR) matrices. Previously, no such algorithm existed, and performing polynomial expansions on CSR matrices…

Data Structures and Algorithms · Computer Science 2018-09-11 Andrew Nystrom , John Hughes

Feature selection aims to identify the optimal feature subset for enhancing downstream models. Effective feature selection can remove redundant features, save computational resources, accelerate the model learning process, and improve the…

Machine Learning · Computer Science 2024-12-19 Nanxu Gong , Wangyang Ying , Dongjie Wang , Yanjie Fu

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…

We study the column subset selection problem with respect to the entrywise $\ell_1$-norm loss. It is known that in the worst case, to obtain a good rank-$k$ approximation to a matrix, one needs an arbitrarily large $n^{\Omega(1)}$ number of…

Data Structures and Algorithms · Computer Science 2020-04-20 Zhao Song , David P. Woodruff , Peilin Zhong

Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…

Numerical Analysis · Computer Science 2016-02-01 Duangpen Jetpipattanapong , Gun Srijuntongsiri

We introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products or inverses. This factorization is a critical part of a…

Numerical Analysis · Mathematics 2019-09-17 Grey Ballard , James Demmel , Ioana Dumitriu , Alexander Rusciano

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…

Numerical Analysis · Computer Science 2017-03-17 Mostafa Rahmani , George Atia