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Related papers: Sparse outlier-robust PCA for multi-source data

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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

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

Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{\`e}s, Wright, Li, and Ma…

Information Theory · Computer Science 2018-08-14 Namrata Vaswani , Praneeth Narayanamurthy

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by…

Methodology · Statistics 2021-01-13 Mia Hubert , Peter J. Rousseeuw , Wannes Van den Bossche

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Machine Learning · Statistics 2019-10-28 Jean P. Chereau , Bruno Scalzo Dees , Danilo P. Mandic

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…

Optimization and Control · Mathematics 2022-02-22 Dimitris Bertsimas , Ryan Cory-Wright , Jean Pauphilet

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

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

Machine Learning · Statistics 2022-09-13 Yuxin Chen , Jianqing Fan , Cong Ma , Yuling Yan

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…

Machine Learning · Computer Science 2022-11-15 Yu Cheng , Ilias Diakonikolas , Rong Ge , Shivam Gupta , Daniel M. Kane , Mahdi Soltanolkotabi

Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert , Gabriele Steidl

The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which…

Methodology · Statistics 2013-08-01 Kaveh Vakili , Eric Schmitt

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

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…

Numerical Analysis · Mathematics 2025-04-28 Yangyang Xu , Kexin Li , Li Yang , You-Wei Wen

Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

Machine Learning · Computer Science 2024-08-23 Yingzhuo Deng , Ke Hu , Bo Li , Yao Zhang

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Machine Learning · Statistics 2023-08-07 Fan Chen , Karl Rohe

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Machine Learning · Statistics 2019-08-21 Genevera I. Allen , Michael Weylandt

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of…

Machine Learning · Statistics 2020-05-08 Peter Richtárik , Majid Jahani , Selin Damla Ahipaşaoğlu , Martin Takáč

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Computer Vision and Pattern Recognition · Computer Science 2020-09-28 Chisom Ezinne Ogbuanya

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…

Methodology · Statistics 2021-04-06 Tiffany M. Tang , Genevera I. Allen

This work studies the recursive robust principal components' analysis (PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this…

Information Theory · Computer Science 2011-06-17 Chenlu Qiu , Namrata Vaswani