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Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…

Systems and Control · Electrical Eng. & Systems 2020-02-27 Davide Beretta , Samuele Grillo , Davide Pigoli , Enea Bionda , Claudio Bossi , Carlo Tornelli

We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition…

Machine Learning · Computer Science 2025-02-27 Fangshuo Liao , Wenyi Su , Anastasios Kyrillidis

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

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

Machine Learning · Statistics 2013-08-09 Kamalika Chaudhuri , Anand D. Sarwate , Kaushik Sinha

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

Statistics Theory · Mathematics 2016-11-26 Dan Shen , Haipeng Shen , J. S. Marron

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

Computer Vision and Pattern Recognition · Computer Science 2010-02-11 Mingyu Fan , Nannan Gu , Hong Qiao , Bo Zhang

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

Methodology · Statistics 2024-10-02 Jianqing Fan , Yuling Yan , Yuheng Zheng

Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…

Methodology · Statistics 2025-10-01 Wenhui Wu , Changchun Shang , Jianhua Zhao , Xuan Ma , Yue Wang

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

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…

Statistics Theory · Mathematics 2019-07-30 Yariv Aizenbud , Barak Sober

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase…

Machine Learning · Statistics 2022-09-08 Zhaoqiang Liu , Jiulong Liu , Subhroshekhar Ghosh , Jun Han , Jonathan Scarlett

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Methodology · Statistics 2025-07-15 Felix Reinbott , Anja Janßen

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

Methodology · Statistics 2018-01-08 Jianqing Fan , Qiang Sun , Wen-Xin Zhou , Ziwei Zhu

For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is…

Machine Learning · Statistics 2021-05-31 Jingxin Zhang , Donghua Zhou , Maoyin Chen

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…

Econometrics · Economics 2024-11-08 Jie Wei , Yonghui Zhang

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

Statistics Theory · Mathematics 2025-08-05 Xin Bing , Marten Wegkamp

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…

Methodology · Statistics 2020-06-24 Ioannis Kalogridis , Stefan Van Aelst

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…

Machine Learning · Statistics 2020-09-04 Young Woong Park , Diego Klabjan

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

Statistics Theory · Mathematics 2022-10-20 Elynn Y. Chen , Jianqing Fan