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Related papers: Parameterized Principal Component Analysis

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Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

Statistics Theory · Mathematics 2010-03-02 Ci-Ren Jiang , Jane-Ling Wang

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional…

Applications · Statistics 2011-04-19 Sungkyu Jung , Mark Foskey , J. S. Marron

In this paper, we use semi-definite programming and generalized principal component analysis (GPCA) to distinguish between two or more different facial expressions. In the first step, semi-definite programming is used to reduce the…

Computer Vision and Pattern Recognition · Computer Science 2009-06-10 Behnood Gholami , Allen R. Tannenbaum , Wassim M. Haddad

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Machine Learning · Statistics 2017-08-16 Darren Homrighausen , Daniel J. McDonald

Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…

Applications · Statistics 2024-09-19 Joshua C. Macdonald , Javier Blanco-Portillo , Marcus W. Feldman , Yoav Ram

We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…

Methodology · Statistics 2019-10-09 Giovanni Maria Merola

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…

Materials Science · Physics 2021-05-26 T. Tula , G. Möller , J. Quintanilla , S. R. Giblin , A. D. Hillier , E. E. McCabe , S. Ramos , D. S. Barker , S. Gibson

This paper compares two neural network input selection schemes, the Principal Component Analysis (PCA) and the Automatic Relevance Determination (ARD) based on Mac-Kay's evidence framework. The PCA takes all the input data and projects it…

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 L. Mdlazi , T. Marwala , C. J. Stander , C. Scheffer , P. S. Heyns

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

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

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…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…

Computer Vision and Pattern Recognition · Computer Science 2018-01-24 Niannan Xue , Jiankang Deng , Shiyang Cheng , Yannis Panagakis , Stefanos Zafeiriou

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Machine Learning · Statistics 2023-08-07 Fan Chen , Karl Rohe

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Machine Learning · Statistics 2019-10-28 Jean P. Chereau , Bruno Scalzo Dees , Danilo P. Mandic

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…

Information Theory · Computer Science 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang

We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…

Machine Learning · Statistics 2017-11-23 Abubakar Abid , Martin J. Zhang , Vivek K. Bagaria , James Zou

Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the…

Applications · Statistics 2024-07-03 Reza Dastranj , Martin Kolar

Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…

Methodology · Statistics 2021-08-12 Xinyu Zhang , Howell Tong

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

Machine Learning · Statistics 2021-06-29 Avishek Chatterjee , Satyaki Mazumder , Koel Das

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