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Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Machine Learning · Computer Science 2017-07-11 Xiaojun Chang , Feiping Nie , Yi Yang , Heng Huang

Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods…

Machine Learning · Computer Science 2025-03-06 Alberto Del Pia , Dekun Zhou , Yinglun Zhu

Natural scene character recognition is challenging due to the cluttered background, which is hard to separate from text. In this paper, we propose a novel method for robust scene character recognition. Specifically, we first use robust…

Computer Vision and Pattern Recognition · Computer Science 2016-06-16 Zheng Zhang , Yong Xu , Cheng-Lin Liu

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

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

In this article we propose a novel face recognition method based on Principal Component Analysis (PCA) and Log-Gabor filters. The main advantages of the proposed method are its simple implementation, training, and very high recognition…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Vytautas Perlibakas

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Statistics Theory · Mathematics 2014-01-08 T. Tony Cai , Zongming Ma , Yihong Wu

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

Methodology · Statistics 2025-10-07 Jan O. Bauer

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most…

Machine Learning · Computer Science 2014-05-02 Zhenfang Hu , Gang Pan , Yueming Wang , Zhaohui Wu

Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…

Computer Vision and Pattern Recognition · Computer Science 2017-05-22 Zhenfang Hu , Gang Pan , Yueming Wang , Zhaohui Wu

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

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 widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

Machine Learning · Computer Science 2018-10-17 Xu Feng , Yuyang Xie , Mingye Song , Wenjian Yu , Jie Tang

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

Machine Learning · Computer Science 2019-05-29 Chun-Mei Feng , Yong Xu , Jin-Xing Liu , Ying-Lian Gao , Chun-Hou Zheng

This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where…

Computer Vision and Pattern Recognition · Computer Science 2023-02-28 HanQin Cai , Keaton Hamm , Longxiu Huang , Deanna Needell

Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…

Machine Learning · Computer Science 2022-01-10 Alberto Del Pia

Face images captured in heterogeneous environments, e.g., sketches generated by the artists or composite-generation software, photos taken by common cameras and infrared images captured by corresponding infrared imaging devices, usually…

Computer Vision and Pattern Recognition · Computer Science 2016-07-04 Chunlei Peng , Xinbo Gao , Nannan Wang , Jie Li

The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…

Methodology · Statistics 2021-05-31 Giovanni Maria Merola

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

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Machine Learning · Computer Science 2019-01-08 Jian Vora