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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

In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…

Statistics Theory · Mathematics 2012-06-04 Karim Lounici

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…

Machine Learning · Statistics 2019-03-28 Shixiang Chen , Shiqian Ma , Lingzhou Xue , Hui Zou

Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model…

Methodology · Statistics 2018-05-18 Ze Jin , Benjamin B. Risk , David S. Matteson

We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…

Methodology · Statistics 2019-10-09 Giovanni Maria Merola

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

Methodology · Statistics 2021-01-22 Xiaoyu Hu , Fang Yao

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

Machine Learning · Statistics 2017-09-19 Clément Elvira , Pierre Chainais , Nicolas Dobigeon

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

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…

Machine Learning · Statistics 2016-10-04 Fang Han , Han Liu

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

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…

Methodology · Statistics 2017-10-03 Benjamin B. Risk , David S. Matteson , David Ruppert

Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers…

Machine Learning · Computer Science 2012-06-22 Sivaraman Balakrishnan , Kriti Puniyani , John Lafferty

In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…

Methodology · Statistics 2022-09-14 Haiyan Jiang , Shanshan Qin , Oscar Hernan Madrid Padilla

Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA works only for two datasets, i.e., there are only two views or two distinct objects. To…

Machine Learning · Computer Science 2020-04-24 Jia Cai , Kexin Lv , Junyi Huo , Xiaolin Huang , Jie Yang

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Methodology · Statistics 2021-12-09 Martin Schlather , Felix Reinbott

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…

Applications · Statistics 2019-04-23 Mohammad Nabhan , Yajun Mei , Jianjun Shi

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…

Machine Learning · Computer Science 2021-01-06 Chihao Zhang , Kuo Gai , Shihua Zhang

This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…

Machine Learning · Statistics 2023-04-07 Hideaki Ishibashi , Shotaro Akaho

In independent component analysis it is assumed that the observed random variables are linear combinations of latent, mutually independent random variables called the independent components. Our model further assumes that only the…

Statistics Theory · Mathematics 2016-12-19 Joni Virta , Klaus Nordhausen , Hannu Oja

Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…

Optimization and Control · Mathematics 2017-12-05 Santanu S. Dey , Rahul Mazumder , Marco Molinaro , Guanyi Wang