English
Related papers

Related papers: A Dictionary-Based Generalization of Robust PCA wi…

200 papers

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled…

Machine Learning · Statistics 2019-06-14 Saiprasad Ravishankar , Brian E. Moore , Raj Rao Nadakuditi , Jeffrey A. Fessler

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Numerical Analysis · Computer Science 2017-04-13 Nematollah Zarmehi , Farokh Marvasti

The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the…

Machine Learning · Statistics 2016-08-24 Xiao Fu , Wing-Kin Ma , José Bioucas-Dias , Tsung-Han Chan

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient…

Machine Learning · Computer Science 2023-06-12 Francesco Tonin , Alex Lambert , Panagiotis Patrinos , Johan A. K. Suykens

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

Machine Learning · Computer Science 2018-10-17 Xu Feng , Yuyang Xie , Mingye Song , Wenjian Yu , Jie Tang

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

Mathematical Software · Computer Science 2015-06-29 François-Henry Rouet , Xiaoye S. Li , Pieter Ghysels , Artem Napov

We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as…

Statistics Theory · Mathematics 2024-04-22 Andrew D. McRae , Justin Romberg , Mark A. Davenport

Advancements in Sonar image capture have opened the door to powerful classification schemes for automatic target recognition (ATR. Recent work has particularly seen the application of sparse reconstruction-based classification (SRC) to…

Computer Vision and Pattern Recognition · Computer Science 2016-01-14 John McKay , Vishal Monga , Raghu Raj

We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and…

Numerical Analysis · Mathematics 2025-06-11 Renjie Xu , Chong Wu , Maolin Che , Zhuoheng Ran , Yimin Wei , Hong Yan

We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…

Optimization and Control · Mathematics 2021-05-26 Robbie Vreugdenhil , Viet Anh Nguyen , Armin Eftekhari , Peyman Mohajerin Esfahani

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Statistics Theory · Mathematics 2019-12-17 Arvind Prasadan , Raj Rao Nadakuditi , Debashis Paul

We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting…

Information Theory · Computer Science 2015-03-20 Liliana Borcea , Thomas Callaghan , George Papanicolaou

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…

Machine Learning · Computer Science 2016-11-30 Cristian Rusu , Nuria Gonzalez-Prelcic , Robert Heath

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based…

Machine Learning · Computer Science 2019-07-22 Canyi Lu , Pan Zhou

Laser-induced breakdown spectroscopy is a preferred technique for fast and direct multi-elemental mapping of samples under ambient pressure, without any limitation on the targeted element. However, LIBS mapping data have two peculiarities:…

Applied Physics · Physics 2022-10-11 Riccardo Finotello , Mohamed Tamaazousti , Jean-Baptiste Sirven

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

Numerical Analysis · Mathematics 2022-03-10 Domitilla Brandoni , Margherita Porcelli , Valeria Simoncini

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Machine Learning · Statistics 2020-11-19 J. Camacho , A. K. Smilde , E. Saccenti , J. A. Westerhuis

This paper presents a sparse representation-based classification approach with a novel dictionary construction procedure. By using the constructed dictionary sophisticated prior knowledge about the spatial nature of the image can be…

Computer Vision and Pattern Recognition · Computer Science 2017-08-22 Ribana Roscher , Björn Waske

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Numerical Analysis · Mathematics 2019-07-12 Jared Tanner , Andrew Thompson , Simon Vary

Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…

Machine Learning · Computer Science 2020-04-20 Majid Janzamin , Rong Ge , Jean Kossaifi , Anima Anandkumar