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Tutorial on PCA and approximate PCA and approximate kernel PCA
Artificial Intelligence Review, 2022 Principal 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 ...
S. Marukatat
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Geodesic PCA in the Wasserstein space by Convex PCA [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2017 We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space of probability measures on the line, with finite second moment, endowed with the Wasserstein metric. We discuss the advantages of this approach, over a standard functional PCA of probability densities in the Hilbert space of square-integrable functions.
Jérémie Bigot +3 more
semanticscholar +6 more sources
Fundamenta Mathematicae, 2000 Summary: Three sets occurring in functional analysis are shown to be of class PCA (also called \(\Sigma_2^1)\) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected.
Robert Kaufman
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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.
Norma Bargary +7 more
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Tangent Phylogenetic PCA [PDF]
, 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 ...
Akhøj, Morten +2 more
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Singular Learning of Deep Multilayer Perceptrons for EEG-Based Emotion Recognition
Frontiers in Computer Science, 2021 Human emotion recognition is an important issue in human–computer interactions, and electroencephalograph (EEG) has been widely applied to emotion recognition due to its high reliability.
Weili Guo +6 more
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Scientific Reports, 2022 Principal Component Analysis (PCA) is a multivariate analysis that reduces the complexity of datasets while preserving data covariance. The outcome can be visualized on colorful scatterplots, ideally with only a minimal loss of information.
E. Elhaik
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IEEE Transactions on Geoscience and Remote Sensing, 2022 As hyperspectral imagery (HSI) contains rich spectral and spatial information, a novel principal component analysis (PCA) and segmented-PCA (SPCA)-based multiscale 2-D-singular spectrum analysis (2-D-SSA) fusion method is proposed for joint spectral ...
Hang Fu +4 more
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Arab Journal of Forensic Sciences & Forensic Medicine, 2023 In the ambit of Forensic examination of the questioned documents, writing instruments often serve as an essential tool in disclosing the legitimacy of a document.
Pawan Gupta +3 more
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Statistics & Risk Modeling, 2012 Abstract Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X 1,...,X n onto the first D eigenvectors of the Principal Component Analysis ...
Biau, Gérard, Mas, André
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