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Tutorial on PCA and approximate PCA and approximate kernel PCA
Artificial Intelligence Review, 2022 AbstractPrincipal Component Analysis (PCA) is one of the most widely used data analysis methods in machine learning and AI. This manuscript focuses on the mathematical foundation of classical PCA and its application to a small-sample-size scenario and a large dataset in a high-dimensional space scenario.
Sanparith Marukatat +1 more
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PCA of waveforms and functional PCA: A primer for biomechanics [PDF]
Journal of Biomechanics, 2021 Principal components analysis (PCA) of waveforms and functional PCA (fPCA) are statistical approaches used to explore patterns of variability in biomechanical curve data, with fPCA being an accepted statistical method grounded within the functional data analysis (FDA) statistical framework.
John Warmenhoven +2 more
exaly +3 more sources
Canadian Journal of Statistics, 2023 AbstractMahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high‐dimensional cases because it balances all orthogonalized covariates equally.
Hengtao Zhang +2 more
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Journal of Statistical Physics, 2017 A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is nearly continuous, any distinction between components that we keep and those that we ignore becomes arbitrary; it then ...
Bradde, Serena, Bialek, William
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RKF-PCA: Robust kernel fuzzy PCA
Neural Networks, 2009 Principal component analysis (PCA) is a mathematical method that reduces the dimensionality of the data while retaining most of the variation in the data. Although PCA has been applied in many areas successfully, it suffers from sensitivity to noise and is limited to linear principal components.
Computer and Information Science and Engineering, University of Florida, United States ( host institution ) +3 more
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, 2023 Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, due to shared evolutionary history. The method works on Euclidean data, but in evolutionary biology there is a need for applying it to data on manifolds, particularly shapes ...
Morten Akhøj +2 more
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SIAM Journal on Imaging Sciences, 2013 We describe a method for analyzing the shape variability of images, called geometric PCA. Our approach is based on the use of deformation operators to model the geometric variability of images around a reference mean pattern. This leads to a new algorithm for estimating shape variability.
Bigot, Jérémie +2 more
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$e$PCA: High dimensional exponential family PCA
The Annals of Applied Statistics, 2018 Many applications, such as photon-limited imaging and genomics, involve large datasets with noisy entries from exponential family distributions. It is of interest to estimate the covariance structure and principal components of the noiseless distribution.
Liu, Lydia T. +2 more
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Validation of Nonlinear PCA [PDF]
Neural Processing Letters, 2012 Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied ...
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DP-PCA: Statistically Optimal and Differentially Private PCA
Advances in Neural Information Processing Systems 35, 2022 We study the canonical statistical task of computing the principal component from $n$ i.i.d.~data in $d$ dimensions under $(\varepsilon,δ)$-differential privacy. Although extensively studied in literature, existing solutions fall short on two key aspects: ($i$) even for Gaussian data, existing private algorithms require the number of samples $n$ to ...
Xiyang Liu +3 more
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