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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

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

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

Numerical Analysis · Mathematics 2017-02-07 Indika Udagedara , Brian Helenbrook , Aaron Luttman , Jared Catenacci

Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed…

Applications · Statistics 2024-11-11 Anahita Nodehi , Mousa Golalizadeh , Mehdi Maadooliat , Claudio Agostinelli

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…

Machine Learning · Statistics 2019-05-22 Charles Bouveyron , Pierre Latouche , Pierre-Alexandre Mattei

Modern mobile health (mHealth) assessment combines self-reported measures of participants' health experiences with passively collected health behavior data throughout the day. These data are collected across multiple measurement scales,…

Methodology · Statistics 2026-03-13 Debangan Dey , Rahul Ghosal , Kathleen Merikangas , Vadim Zipunnikov

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

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Optimization and Control · Mathematics 2022-02-22 Dimitris Bertsimas , Ryan Cory-Wright , Jean Pauphilet

I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…

Econometrics · Economics 2022-05-23 Sung Hoon Choi

The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…

Methodology · Statistics 2024-07-23 Tui Nolan , Sylvia Richardson , Hélène Ruffieux

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Computation · Statistics 2016-01-29 Qiaoya Zhang , Yiyuan She

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Machine Learning · Statistics 2024-07-11 Puoya Tabaghi , Michael Khanzadeh , Yusu Wang , Sivash Mirarab

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…

Machine Learning · Statistics 2026-03-17 Ying Hu , Hu Yang

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Machine Learning · Statistics 2023-02-23 Harry Dong , Tian Tong , Cong Ma , Yuejie Chi

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

Statistics Theory · Mathematics 2009-08-26 Arash A. Amini , Martin J. Wainwright

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Machine Learning · Computer Science 2026-05-05 Mario Sayde , Christopher Khater , Jihad Fahs , Ibrahim Abou-Faycal

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

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

Methodology · Statistics 2020-12-15 Jingxin Zhang , Hao Chen , Songhang Chen , Xia Hong

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

Methodology · Statistics 2024-10-02 Jianqing Fan , Yuling Yan , Yuheng Zheng

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…

Computer Vision and Pattern Recognition · Computer Science 2017-03-29 Niannan Xue , Yannis Panagakis , Stefanos Zafeiriou