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Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in data analysis. The PCA direction is a linear combination of all features with nonzero loadings -- this impedes interpretability. Sparse PCA…

Optimization and Control · Mathematics 2021-08-18 Santanu S. Dey , Rahul Mazumder , Guanyi Wang

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…

Machine Learning · Computer Science 2015-05-05 Shankar Narasimhan , Nirav Bhatt

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

Machine Learning · Statistics 2018-08-24 Clifford Anderson-Bergman , Tamara G. Kolda , Kina Kincher-Winoto

The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…

Optimization and Control · Mathematics 2024-01-02 Yongchun Li , Santanu S. Dey , Weijun Xie

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…

Machine Learning · Computer Science 2016-11-01 Namrata Vaswani , Han Guo

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…

Machine Learning · Computer Science 2016-11-03 Namrata Vaswani , Han Guo

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…

Methodology · Statistics 2023-06-27 Hossein Haghbin , Yue Zhao , Mehdi Maadooliat

In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…

Computation · Statistics 2012-01-18 Hua Zhou , Artin Armagan , David B. Dunson

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…

Machine Learning · Statistics 2014-08-25 Zhaoran Wang , Huanran Lu , Han Liu

We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method. We also discuss the dependent case where the covariance matrix $\Sigma$ is not…

Methodology · Statistics 2016-02-18 T. Tony Cai , Linjun Zhang

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

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Methodology · Statistics 2025-08-22 Zhongyuan Lyu , Ming Yuan

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 a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…

Methodology · Statistics 2013-05-13 Marie Verbanck , Julie Josse , François Husson

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 an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

General Relativity and Quantum Cosmology · Physics 2022-08-17 Sayantani Datta , M. Saleem , K. G. Arun , B. S. Sathyaprakash

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

Methodology · Statistics 2025-02-04 Aihua Li , Surya T. Tokdar , Jason Xu

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

Methodology · Statistics 2023-08-22 Fei Ding , Shiyuan He , David E. Jones , Jianhua Z. Huang

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…

Machine Learning · Computer Science 2014-08-12 David Wipf

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…

Machine Learning · Statistics 2012-07-11 David Wipf