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Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…

Numerical Analysis · Mathematics 2019-03-08 Liron Mor-Yosef , Haim Avron

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

Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…

Computer Vision and Pattern Recognition · Computer Science 2018-01-24 Niannan Xue , Jiankang Deng , Shiyang Cheng , Yannis Panagakis , Stefanos Zafeiriou

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…

Machine Learning · Computer Science 2019-05-28 Lai Tian , Feiping Nie , Xuelong Li

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…

Data Structures and Algorithms · Computer Science 2010-11-02 Jacob Bien , Ya Xu , Michael W. Mahoney

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Statistics Theory · Mathematics 2009-01-29 Iain M Johnstone , Arthur Yu Lu

Data processing constitutes a critical component of high-contrast exoplanet imaging. Its role is almost as important as the choice of a coronagraph or a wavefront control system, and it is intertwined with the chosen observing strategy.…

Instrumentation and Methods for Astrophysics · Physics 2016-04-20 C. A. Gomez Gonzalez , O. Absil , P. -A. Absil , M. Van Droogenbroeck , D. Mawet , J. Surdej

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The…

Computation · Statistics 2024-08-29 Pia Pfeiffer , Laura Vana-Gür , Peter Filzmoser

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…

Statistics Theory · Mathematics 2015-04-06 Chao Gao , Harrison H. Zhou

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…

Methodology · Statistics 2014-08-19 Giovanni Maria Merola

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

Machine Learning · Computer Science 2015-08-03 Ohad Shamir

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…

Machine Learning · Statistics 2021-02-09 HanQin Cai , Keaton Hamm , Longxiu Huang , Jiaqi Li , Tao Wang

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA…

Information Theory · Computer Science 2017-05-30 Huynh Van Luong , Nikos Deligiannis , Jurgen Seiler , Soren Forchhammer , Andre Kaup

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Machine Learning · Statistics 2014-05-09 Dimitris S. Papailiopoulos , Alexandros G. Dimakis , Stavros Korokythakis

Face Recognition is most used for biometric user authentication that identifies a user based on his or her facial features. The system is in high demand, as it is used by many businesses and employed in many devices such as smartphones and…

Computer Vision and Pattern Recognition · Computer Science 2020-11-26 Kavan Adeshara , Vinayak Elangovan

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…

Data Structures and Algorithms · Computer Science 2016-11-24 Kimon Fountoulakis , Abhisek Kundu , Eugenia-Maria Kontopoulou , Petros Drineas

Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is…

Computer Vision and Pattern Recognition · Computer Science 2015-06-04 Meng Yang , Lei Zhang , Jian Yang , David Zhang

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…

Methodology · Statistics 2019-10-09 Giovanni Maria Merola