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Modern vision pipelines increasingly rely on pretrained image encoders whose representations are reused across tasks and models, yet these representations are often overcomplete and model-specific. We propose a simple, training-free method…

Computer Vision and Pattern Recognition · Computer Science 2026-04-02 Dylan B. Lewis , Jens Gregor , Hector Santos-Villalobos

Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the…

Discrete Mathematics · Computer Science 2020-06-17 Uthaipon Tantipongpipat , Samira Samadi , Mohit Singh , Jamie Morgenstern , Santosh Vempala

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…

Materials Science · Physics 2021-05-26 T. Tula , G. Möller , J. Quintanilla , S. R. Giblin , A. D. Hillier , E. E. McCabe , S. Ramos , D. S. Barker , S. Gibson

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

Computer Vision and Pattern Recognition · Computer Science 2019-03-13 Hanli Qiao

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

Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…

Applications · Statistics 2024-12-16 Mariia Legenkaia , Laurent Bourdieu , Rémi Monasson

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by…

Signal Processing · Electrical Eng. & Systems 2022-06-20 Xiaoqiang Hua , Yusuke Ono , Linyu Peng , Yuting Xu

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

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas…

Solar and Stellar Astrophysics · Physics 2015-06-18 Erik Bertram , Rahul Shetty , Simon C. O. Glover , Ralf S. Klessen , Julia Roman-Duval , Christoph Federrath

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

Machine Learning · Statistics 2023-07-21 Debolina Paul , Saptarshi Chakraborty , Swagatam Das

Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…

Quantum Physics · Physics 2021-08-03 Chao-Hua Yu , Fei Gao , Song Lin , Jingbo Wang

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Machine Learning · Computer Science 2022-08-25 Guilherme Dean Pelegrina , Leonardo Tomazeli Duarte

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

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

We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to…

Computer Vision and Pattern Recognition · Computer Science 2010-05-18 Georgios Tzimiropoulos , Stefanos Zafeiriou

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Statistics Theory · Mathematics 2021-04-02 Anru R. Zhang , T. Tony Cai , Yihong Wu

Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for…

Image and Video Processing · Electrical Eng. & Systems 2019-08-27 Benyamin Ghojogh , Fakhri Karray , Mark Crowley

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…

Materials Science · Physics 2022-08-19 T. Tula , G. Möller , J. Quintanilla , S. R. Giblin , A. D. Hillier , E. E. McCabe , S. Ramos , D. S. Barker , S. Gibson

Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model…

Machine Learning · Computer Science 2026-04-22 Alexandre L. M. Levada

A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…

Machine Learning · Statistics 2014-08-22 Alessandro Rudi , Guille D. Canas , Lorenzo Rosasco