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Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

Methodology · Statistics 2023-09-26 Subhrajyoty Roy , Ayanendranath Basu , Abhik Ghosh

In this paper, we analyze the applicability of the principal component analysis (PCA) as a tool to extract the Sq variation of the geomagnetic field. We tested different geomagnetic field components and used data measured at different…

Geophysics · Physics 2022-07-14 Anna Morozova , Rania Rebbah

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

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

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Computation · Statistics 2016-01-29 Qiaoya Zhang , Yiyuan She

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…

Machine Learning · Statistics 2014-07-17 Zhaoyi Kang , Costas J. Spanos

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…

Machine Learning · Statistics 2023-11-14 Javier Salazar Cavazos , Jeffrey A. Fessler , Laura Balzano

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

When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…

Methodology · Statistics 2017-05-30 Sungwon Lee , Sungkyu Jung

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…

Computer Vision and Pattern Recognition · Computer Science 2024-08-06 Nathan Mankovich , Gustau Camps-Valls , Tolga Birdal

Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…

Machine Learning · Computer Science 2025-09-24 Han-Lin Hsieh , Maryam M. Shanechi

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Machine Learning · Computer Science 2019-03-19 Kai Liu , Qiuwei Li , Hua Wang , Gongguo Tang

Matrix factor model has been growing popular in scientific fields such as econometrics, which serves as a two-way dimension reduction tool for matrix sequences. In this article, we for the first time propose the matrix elliptical factor…

Methodology · Statistics 2022-03-29 ZeYu Li , Yong He , Xinbing Kong , Xinsheng Zhang

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Joaquim A. Dente , R. Vilela Mendes

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

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

Computer Vision and Pattern Recognition · Computer Science 2010-02-11 Mingyu Fan , Nannan Gu , Hong Qiao , Bo Zhang

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Optimization and Control · Mathematics 2024-11-11 Yuqing He , Guanyi Wang , Yu Yang

Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…

Applications · Statistics 2024-12-16 Mariia Legenkaia , Laurent Bourdieu , Rémi Monasson

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

Methodology · Statistics 2019-11-20 Yixuan Qiu , Jing Lei , Kathryn Roeder