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Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Machine Learning · Computer Science 2019-01-30 Jia Chen , Gang Wang , Georgios B. Giannakis

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Machine Learning · Computer Science 2023-02-28 HanQin Cai , Jialin Liu , Wotao Yin

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…

Machine Learning · Computer Science 2025-09-30 Nhan Phan , Thu Nguyen , Uyen Dang , Pål Halvorsen , Michael A. Riegler

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Methodology · Statistics 2025-07-15 Felix Reinbott , Anja Janßen

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) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

Machine Learning · Computer Science 2013-10-25 Nikos Karampatziakis , Paul Mineiro

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Numerical Analysis · Mathematics 2021-01-14 Alberto García-González , Antonio Huerta , Sergio Zlotnik , Pedro Díez

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

Machine Learning · Statistics 2016-02-02 Valero Laparra , Sandra Jiménez , Devis Tuia , Gustau Camps-Valls , Jesús Malo

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Methodology · Statistics 2014-01-15 Ngoc Mai Tran , Maria Osipenko , Wolfgang Karl Haerdle

In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…

Machine Learning · Computer Science 2024-03-13 Long He , Ho-Yin Mak

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Machine Learning · Statistics 2015-05-06 Madeleine Udell , Corinne Horn , Reza Zadeh , Stephen Boyd

Principal component analysis (PCA) is an indispensable tool in many learning tasks that finds the best linear representation for data. Classically, principal components of a dataset are interpreted as the directions that preserve most of…

Optimization and Control · Mathematics 2018-03-13 Raphael A. Hauser , Armin Eftekhari , Heinrich F. Matzinger

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Methodology · Statistics 2021-08-17 Tonglin Zhang , Baijian Yang , Qianqian Song , Jing Su

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Machine Learning · Computer Science 2021-03-23 Rui Zhang , Hongyuan Zhang , Xuelong Li

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Machine Learning · Computer Science 2021-11-30 Arpita Gang , Waheed U. Bajwa

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

Machine Learning · Computer Science 2025-12-01 John J. Vastola , Samuel J. Gershman , Kanaka Rajan

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

Methodology · Statistics 2023-09-26 Subhrajyoty Roy , Ayanendranath Basu , Abhik Ghosh

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an…

Image and Video Processing · Electrical Eng. & Systems 2026-02-02 George Webber , Alexander Denker , Riccardo Barbano , Andrew J Reader

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

Machine Learning · Statistics 2022-09-05 Michael Weylandt , George Michailidis

The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…

Machine Learning · Statistics 2020-06-17 Artur Bekasov , Iain Murray