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Related papers: Information-theoretically Optimal Sparse PCA

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Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

Machine Learning · Computer Science 2013-10-25 Nikos Karampatziakis , Paul Mineiro

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

Machine Learning · Statistics 2018-08-24 Clifford Anderson-Bergman , Tamara G. Kolda , Kina Kincher-Winoto

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…

Methodology · Statistics 2026-02-26 Patricia Puchhammer , Ines Wilms , Peter Filzmoser

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

We propose a novel topic discovery algorithm for unlabeled images based on the bag-of-words (BoW) framework. We first extract a dictionary of visual words and subsequently for each image compute a visual word occurrence histogram. We view…

Computer Vision and Pattern Recognition · Computer Science 2013-11-07 Martin Takáč , Selin Damla Ahipaşaoğlu , Ngai-Man Cheung , Peter Richtárik

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

Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In…

Machine Learning · Computer Science 2019-02-08 Qiwei Xie , Liang Tang , Weifu Li , Vijay John , Yong Hu

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The…

Computation · Statistics 2024-08-29 Pia Pfeiffer , Laura Vana-Gür , Peter Filzmoser

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 the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Optimization and Control · Mathematics 2017-07-11 Christopher De Sa , Bryan He , Ioannis Mitliagkas , Christopher Ré , Peng Xu

We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…

Machine Learning · Statistics 2023-02-28 Matthäus Kleindessner , Michele Donini , Chris Russell , Muhammad Bilal Zafar

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from…

Machine Learning · Statistics 2015-05-12 Shuichi Kawano , Hironori Fujisawa , Toyoyuki Takada , Toshihiko Shiroishi

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

Optimization and Control · Mathematics 2018-12-11 Jianchao Bai , Hongchao Zhang , Jicheng Li

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is…

Machine Learning · Statistics 2009-09-09 Rodolphe Jenatton , Guillaume Obozinski , Francis Bach

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

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

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

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…

Machine Learning · Statistics 2026-03-17 Ying Hu , Hu Yang