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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

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Machine Learning · Computer Science 2026-02-05 Thomas Uriot , Elise Chung

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…

Statistics Theory · Mathematics 2012-02-24 Tom M. W. Nye

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…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

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), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Machine Learning · Computer Science 2022-08-25 Guilherme Dean Pelegrina , Leonardo Tomazeli Duarte

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Machine Learning · Statistics 2022-08-18 Alexander Ritchie , Laura Balzano , Daniel Kessler , Chandra S. Sripada , Clayton Scott

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…

Instrumentation and Methods for Astrophysics · Physics 2015-06-11 Stephen Bailey

In 2019, Yoshida et al. introduced a notion of tropical principal component analysis (PCA). The output is a tropical polytope with a fixed number of vertices that best fits the data. We here apply tropical PCA to dimension reduction and…

Combinatorics · Mathematics 2019-11-26 Robert Page , Leon Zhang , Ruriko Yoshida

Data collection often results in records that have missing values or variables. This investigation compares 3 different data imputation models and identifies their merits by using accuracy measures. Autoencoder Neural Networks, Principal…

Artificial Intelligence · Computer Science 2007-09-18 Vukosi N. Marivate , Fulufhelo V. Nelwamodo , Tshilidzi Marwala

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Machine Learning · Statistics 2013-10-01 Gonzalo Mateos , Georgios B. Giannakis

Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-14 Tarek Elgamal , Mohamed Hefeeda

Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…

Quantitative Methods · Quantitative Biology 2015-08-24 H. Robert Frost , Zhigang Li , Jason H. Moore

This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…

Data Analysis, Statistics and Probability · Physics 2021-02-24 David Yevick

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

General Relativity and Quantum Cosmology · Physics 2022-08-17 Sayantani Datta , M. Saleem , K. G. Arun , B. S. Sathyaprakash

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

Machine Learning · Statistics 2010-05-14 Huan Xu , Constantine Caramanis , Shie Mannor

Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…

Machine Learning · Computer Science 2022-02-15 Petra Poklukar , Vladislav Polianskii , Anastasia Varava , Florian Pokorny , Danica Kragic

Predictive modeling from high-dimensional genomic data is often preceded by a dimension reduction step, such as principal components analysis (PCA). However, the application of PCA is not straightforward for multi-source data, wherein…

Quantitative Methods · Quantitative Biology 2017-07-19 Adam Kaplan , Eric F. Lock

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Computation · Statistics 2023-11-06 Olga Dorabiala , Aleksandr Aravkin , J. Nathan Kutz

Evaluating the quality of learned representations without relying on a downstream task remains one of the challenges in representation learning. In this work, we present Geometric Component Analysis (GeomCA) algorithm that evaluates…

Machine Learning · Computer Science 2021-05-27 Petra Poklukar , Anastasia Varava , Danica Kragic