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Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

计算工程、金融与科学 · 计算机科学 2021-06-09 Felipe L. Gewers , Gustavo R. Ferreira , Henrique F. de Arruda , Filipi N. Silva , Cesar H. Comin , Diego R. Amancio , Luciano da F. Costa

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

统计理论 · 数学 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

机器学习 · 计算机科学 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

统计理论 · 数学 2009-01-29 Iain M Johnstone , Arthur Yu Lu

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

统计计算 · 统计学 2011-12-23 Nathan Halko , Per-Gunnar Martinsson , Yoel Shkolnisky , Mark Tygert

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

机器学习 · 计算机科学 2017-12-13 Haitao Zhao

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…

机器学习 · 计算机科学 2013-10-25 Nikos Karampatziakis , Paul Mineiro

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

信息论 · 计算机科学 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang

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…

定量方法 · 定量生物学 2018-10-18 Luigi Leonardo Palese

The present paper applied Principal Component Analysis (PCA) for grouping of machines and parts so that the part families can be processed in the cells formed by those associated machines. An incidence matrix with binary entries has been…

适应与自组织系统 · 物理学 2012-02-27 Manojit Chattopadhyay , Surajit Chattopadhyay , Pranab K Dan

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

统计计算 · 统计学 2018-11-06 Victor Minden , Cengiz Pehlevan , Dmitri B. Chklovskii

Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…

统计方法学 · 统计学 2013-05-13 Marie Verbanck , Julie Josse , François Husson

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

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…

天体物理仪器与方法 · 物理学 2015-06-11 Stephen Bailey

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

统计力学 · 物理学 2026-03-31 Mihir Metkar , Neha Sah , Yichen Zhou

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

机器学习 · 统计学 2017-05-19 Xianghui Luo , Robert J. Durrant

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

计算机视觉与模式识别 · 计算机科学 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

统计方法学 · 统计学 2025-08-22 Zhongyuan Lyu , Ming Yuan

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

统计理论 · 数学 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler
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