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In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…

Statistics Theory · Mathematics 2012-06-04 Karim Lounici

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Statistics Theory · Mathematics 2013-05-27 Zongming Ma

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

Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in…

Statistics Theory · Mathematics 2018-11-27 Guy Bresler , Sung Min Park , Madalina Persu

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Machine Learning · Statistics 2021-09-10 Shaojie Xu , Joel Vaughan , Jie Chen , Agus Sudjianto , Vijayan Nair

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of…

Artificial Intelligence · Computer Science 2008-10-08 Ronny Luss , Alexandre d'Aspremont

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Machine Learning · Statistics 2015-05-06 Madeleine Udell , Corinne Horn , Reza Zadeh , Stephen Boyd

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 component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

Optimization and Control · Mathematics 2017-03-09 Amir Beck , Yakov Vaisbourd

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Machine Learning · Statistics 2017-05-19 Xianghui Luo , Robert J. Durrant

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…

Statistics Theory · Mathematics 2011-04-22 Dan Shen , Haipeng Shen , J. S. Marron

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

Optimization and Control · Mathematics 2019-12-24 Raphael A. Hauser , Armin Eftekhari

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Machine Learning · Computer Science 2025-04-07 Long Chen , Xianchao Xiu

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

The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…

Methodology · Statistics 2021-05-31 Giovanni Maria Merola

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Machine Learning · Computer Science 2023-01-25 Arpita Gang , Waheed U. Bajwa

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

Machine Learning · Computer Science 2026-03-03 Difei Cheng , Qiao Hu

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Machine Learning · Statistics 2013-10-01 Gonzalo Mateos , Georgios B. Giannakis