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We formulate a $p$-adic optimisation problem on matrix factorisation, and investigate a heuristic method for it analogous to PCA.

Number Theory · Mathematics 2026-03-13 Tomoki Mihara

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…

Machine Learning · Statistics 2019-08-14 Vittorio Lippi , Giacomo Ceccarelli

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…

Machine Learning · Computer Science 2025-09-30 Nhan Phan , Thu Nguyen , Uyen Dang , Pål Halvorsen , Michael A. Riegler

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Computer Vision and Pattern Recognition · Computer Science 2014-09-02 Quan Wang

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

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…

Machine Learning · Computer Science 2012-04-04 Matthias Scholz

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

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 by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Applications · Statistics 2019-02-12 Stefania Russo , Guangyu Li , Kris Villez

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

Machine Learning · Statistics 2023-12-19 Xuan Ma , Jianhua Zhao , Yue Wang

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

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However,…

Computer Vision and Pattern Recognition · Computer Science 2021-06-25 Abdolrahman Khoshrou , Eric J. Pauwels

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

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Machine Learning · Computer Science 2023-02-28 HanQin Cai , Jialin Liu , Wotao Yin

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Methodology · Statistics 2015-08-20 Vincent Audigier , François Husson , Julie Josse

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Machine Learning · Statistics 2020-11-19 J. Camacho , A. K. Smilde , E. Saccenti , J. A. Westerhuis

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of…

Methodology · Statistics 2015-04-28 Michel Tenenhaus , Arthur Tenenhaus , Patrick J. F. Groenen

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Machine Learning · Statistics 2013-10-01 Gonzalo Mateos , Georgios B. Giannakis

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Methodology · Statistics 2022-11-08 Ayisha Fayomi , Yannis Pantazis , Michail Tsagris , Andrew T. A. Wood

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…

Methodology · Statistics 2016-02-29 Wen-Ting Wang , Hsin-Cheng Huang