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Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…

数值分析 · 数学 2019-03-08 Liron Mor-Yosef , Haim Avron

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

统计方法学 · 统计学 2026-03-24 Daning Bi , Le Chang , Yanrong Yang

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…

统计计算 · 统计学 2016-01-29 Qiaoya Zhang , Yiyuan She

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

统计方法学 · 统计学 2015-06-16 A. A. Akinduko , A. N. Gorban

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…

统计方法学 · 统计学 2026-03-17 Liangliang Yuan , Lei Wang , Quan Kong , Liuhua Peng

In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…

机器学习 · 统计学 2023-06-26 Vlad Niculae

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…

机器学习 · 计算机科学 2021-01-06 Chihao Zhang , Kuo Gai , Shihua Zhang

Deep learning based semi-supervised learning (SSL) methods have achieved strong performance in medical image segmentation, which can alleviate doctors' expensive annotation by utilizing a large amount of unlabeled data. Unlike most existing…

图像与视频处理 · 电气工程与系统科学 2022-07-26 Zihang Xu , Zhenghua Xu , Shuo Zhang , Thomas Lukasiewicz

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…

统计方法学 · 统计学 2025-07-15 Felix Reinbott , Anja Janßen

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…

统计理论 · 数学 2019-07-30 Yariv Aizenbud , Barak Sober

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…

机器学习 · 计算机科学 2013-05-31 Yi-Hao Kao , Benjamin Van Roy

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…

机器学习 · 统计学 2026-01-22 Kexin Wang , Salil Bhate , João M. Pereira , Joe Kileel , Matylda Figlerowicz , Anna Seigal

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…

统计方法学 · 统计学 2023-09-26 Subhrajyoty Roy , Ayanendranath Basu , Abhik Ghosh

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

机器学习 · 计算机科学 2023-01-25 Maxime Haddouche , Benjamin Guedj , John Shawe-Taylor

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

最优化与控制 · 数学 2025-12-02 Ryan Cory-Wright , Jean Pauphilet

Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on…

机器学习 · 计算机科学 2014-04-07 Jonathon Shlens

The ability to reconstruct fine-grained network session data, including individual packets, from coarse-grained feature vectors is crucial for improving network security models. However, the large-scale collection and storage of raw network…

机器学习 · 计算机科学 2025-04-16 Mark Cheung , Sridhar Venkatesan

Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…

统计方法学 · 统计学 2026-05-29 Fabio Centofanti , Mia Hubert , Peter J. Rousseeuw

Ambiguous Medical Image Segmentation (AMIS) is significant to address the challenges of inherent uncertainties from image ambiguities, noise, and subjective annotations. Existing conditional variational autoencoder (cVAE)-based methods…

计算机视觉与模式识别 · 计算机科学 2026-03-16 Xiangyu Li , Chenglin Wang , Qiantong Shen , Fanding Li , Wei Wang , Kuanquan Wang , Yi Shen , Baochun Zhao , Gongning Luo

Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…

统计方法学 · 统计学 2012-12-27 Tomokazu Konishi