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Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Methodology · Statistics 2022-11-08 Ayisha Fayomi , Yannis Pantazis , Michail Tsagris , Andrew T. A. Wood

In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…

Statistics Theory · Mathematics 2016-03-10 Alberto Ohashi , Alexandre B Simas

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Machine Learning · Computer Science 2019-11-19 Samuele Battaglino , Erdem Koyuncu

Principal component analysis (PCA) is not only a fundamental dimension reduction method, but is also a widely used network anomaly detection technique. Traditionally, PCA is performed in a centralized manner, which has poor scalability for…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-12-22 Ni An , Steven Weber

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

Computational Complexity · Computer Science 2007-05-23 Maxim Makatchev

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Statistics Theory · Mathematics 2013-05-27 Zongming Ma

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…

Biological Physics · Physics 2017-04-26 Serena Bradde , William Bialek

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection…

Machine Learning · Statistics 2022-08-03 Benyamin Ghojogh , Mark Crowley

Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…

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 has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…

Quantum Physics · Physics 2022-01-26 Zhaokai Li , Zihua Chai , Yuhang Guo , Wentao Ji , Mengqi Wang , Fazhan Shi , Ya Wang , Seth Lloyd , Jiangfeng Du

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

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

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

Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as…

Methodology · Statistics 2026-04-03 Joseph Sartini , Xinkai Zhou , Liz Selvin , Scott Zeger , Ciprian Crainiceanu

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

Mathematical Software · Computer Science 2013-12-24 W. Liu , H. Zhang , D. Tao , Y. Wang , K. Lu

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Methodology · Statistics 2025-08-22 Zhongyuan Lyu , Ming Yuan

We propose to directly compute classification estimates by learning features encoded with their class scores using PCA. Our resulting model has a encoder-decoder structure suitable for supervised learning, it is computationally efficient…

Machine Learning · Computer Science 2022-10-27 Rozenn Dahyot

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

We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…

Methodology · Statistics 2017-03-28 Yue Selena Niu , Ning Hao , Bin Dong