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Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

Information Theory · Computer Science 2014-05-06 Yash Deshpande , Andrea Montanari

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

Statistics Theory · Mathematics 2009-01-22 Boaz Nadler

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

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 traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…

Quantum Physics · Physics 2026-05-28 Yewei Yuan , Michele Minervini , Mark M. Wilde , Nana Liu

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

Machine Learning · Statistics 2021-11-22 Shuichi Kawano

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Optimization and Control · Mathematics 2024-11-11 Yuqing He , Guanyi Wang , Yu Yang

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Machine Learning · Computer Science 2022-08-25 Guilherme Dean Pelegrina , Leonardo Tomazeli Duarte

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Computer Vision and Pattern Recognition · Computer Science 2012-12-03 Qian Zhao , Deyu Meng , Zongben Xu

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 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

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Statistics Theory · Mathematics 2014-01-08 T. Tony Cai , Zongming Ma , Yihong Wu

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 PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Computation · Statistics 2018-01-11 Jianqing Fan , Dong Wang , Kaizheng Wang , Ziwei Zhu

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

Machine Learning · Statistics 2011-06-23 Alfredo A. Kalaitzis , Neil D. Lawrence

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

Methodology · Statistics 2018-01-08 Jianqing Fan , Qiang Sun , Wen-Xin Zhou , Ziwei Zhu

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Methodology · Statistics 2022-11-08 Ayisha Fayomi , Yannis Pantazis , Michail Tsagris , Andrew T. A. Wood

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

Mathematical Software · Computer Science 2013-12-24 W. Liu , H. Zhang , D. Tao , Y. Wang , K. Lu