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We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…

Statistics Theory · Mathematics 2024-03-27 Roberto I. Oliveira , Zoraida F. Rico

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…

Machine Learning · Statistics 2016-10-04 Fang Han , Han Liu

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

Applications · Statistics 2010-11-17 Seokho Lee , Jianhua Z. Huang , Jianhua Hu

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Methodology · Statistics 2024-01-11 Caren Marzban , Ulvi Yurtsever , Michael Richman

This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this…

Information Theory · Computer Science 2011-03-03 Chenlu Qiu , Namrata Vaswani

Principal component analysis is a simple yet useful dimensionality reduction technique in modern machine learning pipelines. In consequential domains such as college admission, healthcare and credit approval, it is imperative to take into…

Machine Learning · Computer Science 2022-02-08 Hieu Vu , Toan Tran , Man-Chung Yue , Viet Anh Nguyen

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…

Methodology · Statistics 2026-02-26 Patricia Puchhammer , Ines Wilms , Peter Filzmoser

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Applications · Statistics 2025-06-25 Theodosios Papazoglou , Guosheng Yin

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal…

Statistics Theory · Mathematics 2016-12-26 Amelia Perry , Alexander S. Wein , Afonso S. Bandeira , Ankur Moitra

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Machine Learning · Statistics 2015-06-02 Anastasia Podosinnikova , Simon Setzer , Matthias Hein

Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…

Quantum Physics · Physics 2022-01-26 Zhaokai Li , Zihua Chai , Yuhang Guo , Wentao Ji , Mengqi Wang , Fazhan Shi , Ya Wang , Seth Lloyd , Jiangfeng Du

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Methodology · Statistics 2026-03-17 Liangliang Yuan , Lei Wang , Quan Kong , Liuhua Peng

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…

Machine Learning · Computer Science 2021-01-06 Chihao Zhang , Kuo Gai , Shihua Zhang

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…

Machine Learning · Statistics 2015-05-13 Ami Wiesel , Alfred O. Hero

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Numerical Analysis · Mathematics 2021-02-02 Ningyu Sha , Lei Shi , Ming Yan

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…

Machine Learning · Computer Science 2021-05-20 Anish Agarwal , Devavrat Shah , Dennis Shen , Dogyoon Song

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS…

Methodology · Statistics 2015-09-25 E. Schmitt , K. Vakili

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

Machine Learning · Computer Science 2026-03-10 Zhenyu Wang , Molei Liu , Jing Lei , Francis Bach , Zijian Guo

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Statistics Theory · Mathematics 2021-04-02 Anru R. Zhang , T. Tony Cai , Yihong Wu

Statistical machine learning often uses probabilistic algorithms, such as Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Many accelerators are proposed using specialized hardware to address sampling inefficiency, the…

Signal Processing · Electrical Eng. & Systems 2020-03-09 Xiangyu Zhang , Sayan Mukherjee , Alvin R. Lebeck