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The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR…

Machine Learning · Statistics 2019-12-09 Cong Xu , Min Yang , Jin Zhang

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

This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…

Methodology · Statistics 2025-08-08 Zhaoxing Gao

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…

Machine Learning · Statistics 2014-02-20 Fang Han , Han Liu

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Computation · Statistics 2010-06-04 Vladimir Rokhlin , Arthur Szlam , Mark Tygert

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…

Machine Learning · Statistics 2024-01-17 Jasin Machkour , Arnaud Breloy , Michael Muma , Daniel P. Palomar , Frédéric Pascal

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

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

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

Quantitative Methods · Quantitative Biology 2018-10-18 Luigi Leonardo Palese

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

Sparse principal component analysis (PCA) improves interpretability of the classic PCA by introducing sparsity into the dimension-reduction process. Optimization models for sparse PCA, however, are generally non-convex, non-smooth and more…

Optimization and Control · Mathematics 2024-01-09 Lei Wang , Xin Liu , Yin Zhang

We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…

Machine Learning · Statistics 2023-02-28 Matthäus Kleindessner , Michele Donini , Chris Russell , Muhammad Bilal Zafar

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…

Signal Processing · Electrical Eng. & Systems 2023-07-13 Elizabeth Z. C. Tan , Caroline Chaux , Emmanuel Soubies , Vincent Y. F. Tan

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

In this paper, we propose a new method to perform Sparse Kernel Principal Component Analysis (SKPCA) and also mathematically analyze the validity of SKPCA. We formulate SKPCA as a constrained optimization problem with elastic net…

Machine Learning · Computer Science 2018-09-17 Rudrajit Das , Aditya Golatkar , Suyash P. Awate

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

We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-16 Wenda Chu

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

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

Machine Learning · Statistics 2012-02-14 Genevera I. Allen

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Methodology · Statistics 2021-12-09 Martin Schlather , Felix Reinbott