English
Related papers

Related papers: Spatial Sign based Principal Component Analysis fo…

200 papers

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

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Machine Learning · Computer Science 2015-02-25 Malik Magdon-Ismail , Christos Boutsidis

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Machine Learning · Statistics 2021-09-10 Shaojie Xu , Joel Vaughan , Jie Chen , Agus Sudjianto , Vijayan Nair

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

Machine Learning · Computer Science 2019-04-16 Bowen Zhao , Xi Xiao , Wanpeng Zhang , Bin Zhang , Shutao Xia

Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

Statistics Theory · Mathematics 2024-12-17 Hung Hung , Chi-Chun Yeh , Su-Yun Huang

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Machine Learning · Computer Science 2019-03-19 Kai Liu , Qiuwei Li , Hua Wang , Gongguo Tang

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Machine Learning · Computer Science 2023-01-25 Arpita Gang , Waheed U. Bajwa

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

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…

Machine Learning · Statistics 2017-02-24 Soheil Feizi , David Tse

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied…

Methodology · Statistics 2022-04-12 Alexander Dürre , Daniel Vogel , Roland Fried

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

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Statistics Theory · Mathematics 2019-12-17 Arvind Prasadan , Raj Rao Nadakuditi , Debashis Paul

Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

Information Theory · Computer Science 2014-05-06 Yash Deshpande , Andrea Montanari

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

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Methodology · Statistics 2026-03-17 Liangliang Yuan , Lei Wang , Quan Kong , Liuhua Peng

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Machine Learning · Computer Science 2021-11-30 Arpita Gang , Waheed U. Bajwa

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Machine Learning · Computer Science 2019-10-14 Jochen Görtler , Thilo Spinner , Dirk Streeb , Daniel Weiskopf , Oliver Deussen

Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

Machine Learning · Computer Science 2016-01-12 Bo Xie , Yingyu Liang , Le Song

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…

Methodology · Statistics 2020-12-04 Graciela Boente , Matias Salibian-Barrera