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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) 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

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

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

Methodology · Statistics 2021-01-22 Xiaoyu Hu , Fang Yao

Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…

Machine Learning · Computer Science 2022-01-10 Alberto Del Pia

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

Machine Learning · Computer Science 2019-05-29 Chun-Mei Feng , Yong Xu , Jin-Xing Liu , Ying-Lian Gao , Chun-Hou Zheng

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

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

Optimization and Control · Mathematics 2022-10-14 Dimitris Bertsimas , Driss Lahlou Kitane

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…

Statistics Theory · Mathematics 2022-02-09 Joshua Agterberg , Jeremias Sulam

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Optimization and Control · Mathematics 2010-12-24 Youwei Zhang , Alexandre d'Aspremont , Laurent El Ghaoui

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue…

Machine Learning · Statistics 2009-10-13 Bharath Sriperumbudur , David Torres , Gert Lanckriet

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Computer Vision and Pattern Recognition · Computer Science 2020-09-28 Chisom Ezinne Ogbuanya

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 component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Computational Engineering, Finance, and Science · Computer Science 2021-06-09 Felipe L. Gewers , Gustavo R. Ferreira , Henrique F. de Arruda , Filipi N. Silva , Cesar H. Comin , Diego R. Amancio , Luciano da F. Costa

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most…

Machine Learning · Computer Science 2014-05-02 Zhenfang Hu , Gang Pan , Yueming Wang , Zhaohui Wu

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) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Machine Learning · Computer Science 2017-10-27 Gang Wang , Jia Chen , Georgios B. Giannakis

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…

Machine Learning · Computer Science 2014-12-22 Pengtao Xie , Eric Xing

Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…

Methodology · Statistics 2020-12-09 Ruiping Liu , Ndeye Niang , Gilbert Saporta , Huiwen Wang

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

Information Theory · Computer Science 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang