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In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Optimization and Control · Mathematics 2008-12-01 Michel Journée , Yurii Nesterov , Peter Richtárik , Rodolphe Sepulchre

Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to…

Machine Learning · Computer Science 2021-03-02 Adam Farooq , Yordan P. Raykov , Petar Raykov , Max A. Little

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

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

Statistics Theory · Mathematics 2021-12-02 David Hong , Kyle Gilman , Laura Balzano , Jeffrey A. Fessler

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Machine Learning · Statistics 2020-08-11 Keishi Sando , Hideitsu Hino

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

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Methodology · Statistics 2014-01-15 Ngoc Mai Tran , Maria Osipenko , Wolfgang Karl Haerdle

We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by…

Methodology · Statistics 2024-11-18 Yu Lu , Xinkai Zhou , Erjia Cui , Dustin Rogers , Ciprian M. Crainiceanu , Julia Wrobel , Andrew Leroux

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…

Methodology · Statistics 2014-08-19 Giovanni Maria Merola

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…

Machine Learning · Statistics 2019-05-28 Adam Farooq , Yordan P. Raykov , Luc Evers , Max A. Little

The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian…

Machine Learning · Statistics 2020-01-27 Carlos Sevilla-Salcedo , Vanessa Gómez-Verdejo , Pablo M. Olmos

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…

Statistics Theory · Mathematics 2015-04-06 Chao Gao , Harrison H. Zhou

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential echniques cannot be…

Computation · Statistics 2013-05-29 Simon R. White , Theodore Kypraios , Simon P. Preston

When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…

Methodology · Statistics 2018-12-13 Xiongtao Dai , Zhenhua Lin , Hans-Georg Müller

We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…

Methodology · Statistics 2015-09-04 Roman A. Jandarov , Lianne A. Sheppard , Paul D. Sampson , Adam A. Szpiro

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

Methodology · Statistics 2026-03-24 Daning Bi , Le Chang , Yanrong Yang

We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…

Methodology · Statistics 2015-01-21 Kehui Chen , Jing Lei

The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…

Methodology · Statistics 2021-01-25 Mark Girolami , Eky Febrianto , Ge Yin , Fehmi Cirak

Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…

Applications · Statistics 2020-05-19 Phuong T. Vu , Timothy V. Larson , Adam A. Szpiro