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Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

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…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…

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…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

We propose a kernel-PCA based method to detect anomaly in chemical sensors. We use temporal signals produced by chemical sensors to form vectors to perform the Principal Component Analysis (PCA). We estimate the kernel-covariance matrix of…

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…

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)…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…