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Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

Machine Learning · Statistics 2023-07-21 Debolina Paul , Saptarshi Chakraborty , Swagatam Das

In this paper, we propose a low complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all…

Quantum Physics · Physics 2021-01-14 Chen He , Jiazhen Li , Weiqi Liu , Z. Jane Wang

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Applications · Statistics 2025-06-25 Theodosios Papazoglou , Guosheng Yin

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

Methodology · Statistics 2012-02-14 Carlos A. Alfaro , Burcu Aydın , Elizabeth Bullitt , Alim Ladha , Carlos E. Valencia

Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…

Machine Learning · Statistics 2020-09-08 Andrew J. Landgraf , Yoonkyung Lee

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

Machine Learning · Computer Science 2016-01-12 Bo Xie , Yingyu Liang , Le Song

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Methodology · Statistics 2024-01-11 Caren Marzban , Ulvi Yurtsever , Michael Richman

Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…

Machine Learning · Computer Science 2019-07-08 F. William Townes

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

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

Machine Learning · Computer Science 2017-12-13 Haitao Zhao

Single-cell RNA sequencing (scRNA-seq) has revolutionized our ability to analyze gene expression at the cellular level. By providing data on gene expression for each individual cell, scRNA-seq generates large datasets with thousands of…

Computational Complexity · Computer Science 2025-02-11 Md Romizul Islam , Swakkhar Shatabda

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

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Machine Learning · Statistics 2019-05-20 Davoud Ataee Tarzanagh , Mohamad Kazem Shirani Faradonbeh , George Michailidis

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state…

In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…

Methodology · Statistics 2022-04-05 Lingyu He , Yanrong Yang , Bo Zhang

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

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

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 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