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Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Methodology · Statistics 2022-08-18 Xiaoyu Hu , Fang Yao

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

Methodology · Statistics 2021-01-01 Clara Happ , Fabian Scheipl , Alice-Agnes Gabriel , Sonja Greven

This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…

Methodology · Statistics 2025-08-08 Zhaoxing Gao

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Machine Learning · Computer Science 2023-02-23 Francesco Tonin , Qinghua Tao , Panagiotis Patrinos , Johan A. K. Suykens

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

The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR…

Machine Learning · Statistics 2019-12-09 Cong Xu , Min Yang , Jin Zhang

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…

Statistics Theory · Mathematics 2011-04-22 Dan Shen , Haipeng Shen , J. S. Marron

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…

Machine Learning · Computer Science 2024-10-28 Zelin Ren , Xuebing Yang , Yuchen Jiang , Wensheng Zhang

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

Optimization and Control · Mathematics 2022-10-14 Dimitris Bertsimas , Driss Lahlou Kitane

Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…

Methodology · Statistics 2022-05-17 Chetkar Jha , Ian Barnett

We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…

Statistics Theory · Mathematics 2019-01-21 Vladimir Koltchinskii , Matthias Löffler , Richard Nickl

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Machine Learning · Statistics 2022-08-18 Alexander Ritchie , Laura Balzano , Daniel Kessler , Chandra S. Sripada , Clayton Scott

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…

Machine Learning · Statistics 2024-01-17 Jasin Machkour , Arnaud Breloy , Michael Muma , Daniel P. Palomar , Frédéric Pascal

Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…

Machine Learning · Computer Science 2024-10-15 Sharon Hendy , Yehuda Dar

Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the…

Machine Learning · Statistics 2016-02-17 Nan Lin , Junhai Jiang , Shicheng Guo , Momiao Xiong

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

Machine Learning · Statistics 2014-05-14 David Lopez-Paz , Suvrit Sra , Alex Smola , Zoubin Ghahramani , Bernhard Schölkopf

Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted…

Methodology · Statistics 2022-11-29 Shuhao Jiao , Ron D. Frostig , Hernando Ombao

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…

Computation · Statistics 2018-01-11 Jianqing Fan , Dong Wang , Kaizheng Wang , Ziwei Zhu

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Machine Learning · Statistics 2017-05-19 Xianghui Luo , Robert J. Durrant

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Machine Learning · Computer Science 2017-10-27 Gang Wang , Jia Chen , Georgios B. Giannakis