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Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

Machine Learning · Computer Science 2024-08-23 Yingzhuo Deng , Ke Hu , Bo Li , Yao Zhang

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

This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…

Machine Learning · Statistics 2023-04-07 Hideaki Ishibashi , Shotaro Akaho

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…

Methodology · Statistics 2015-06-16 A. A. Akinduko , A. N. Gorban

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

Machine Learning · Computer Science 2019-04-16 Bowen Zhao , Xi Xiao , Wanpeng Zhang , Bin Zhang , Shutao Xia

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

Machine Learning · Statistics 2017-09-19 Clément Elvira , Pierre Chainais , Nicolas Dobigeon

Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…

Artificial Intelligence · Computer Science 2012-07-03 Peratham Wiriyathammabhum , Boonserm Kijsirikul

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

Machine Learning · Statistics 2011-06-23 Alfredo A. Kalaitzis , Neil D. Lawrence

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Applications · Statistics 2019-02-12 Stefania Russo , Guangyu Li , Kris Villez

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…

Methodology · Statistics 2016-01-29 Yiyuan She , Shijie Li , Dapeng Wu

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Statistics Theory · Mathematics 2019-06-27 Holger Drees , Anne Sabourin

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 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…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Machine Learning · Computer Science 2019-11-19 Samuele Battaglino , Erdem Koyuncu

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

Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…

Data Structures and Algorithms · Computer Science 2017-04-26 Wenjian Yu , Yu Gu , Jian Li , Shenghua Liu , Yaohang Li

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Optimization and Control · Mathematics 2009-07-14 Zhaosong Lu , Yong Zhang

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Statistics Theory · Mathematics 2020-06-11 Kristoffer Hellton , Magne Thoresen

Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…

Astrophysics · Physics 2007-05-23 I. Ferreras , B. Rogers , O. Lahav , .

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Methodology · Statistics 2021-12-09 Martin Schlather , Felix Reinbott