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Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

Methodology · Statistics 2026-02-10 Enes Makalic , Daniel F. Schmidt

We present the details of predicting atmospheric turbulence by mining Zernike moment data obtained from simulations as well as experiments. Temporally correlated optical wave-fronts were simulated such that they followed Kolmogorov phase…

Instrumentation and Methods for Astrophysics · Physics 2011-09-14 Akondi Vyas , M. B. Roopashree , B. Raghavendra Prasad

Context. Machine-Learning (ML) solves problems by learning patterns from data, with limited or no human guidance. In Astronomy, it is mainly applied to large observational datasets, e.g. for morphological galaxy classification. Aims. We…

Astrophysics of Galaxies · Physics 2016-04-27 Mario Pasquato , Chul Chung

Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the…

Chemical Physics · Physics 2019-05-22 Michele Ceriotti

Ensemble forecast based on physics-informed models is one of the most widely used forecast algorithms for complex turbulent systems. A major difficulty in such a method is the model error that is ubiquitous in practice. Data-driven machine…

Atmospheric and Oceanic Physics · Physics 2021-11-24 Nan Chen , Yingda Li

Given the increasing complexity of omics datasets, a key challenge is not only improving classification performance but also enhancing the transparency and reliability of model decisions. Effective model performance and feature selection…

Machine Learning · Computer Science 2025-05-07 Diego Perazzolo , Pietro Fanton , Ilaria Barison , Marny Fedrigo , Annalisa Angelini , Chiara Castellani , Enrico Grisan

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

While machine learning (ML) methods have received a lot of attention in recent years, these methods are primarily for prediction. Empirical researchers conducting policy evaluations are, on the other hand, pre-occupied with causal problems,…

Machine Learning · Statistics 2019-03-04 Noemi Kreif , Karla DiazOrdaz

The integration of machine learning (ML) models enhances the efficiency, affordability, and reliability of feature detection in microscopy, yet their development and applicability are hindered by the dependency on scarce and often flawed…

Computer Vision and Pattern Recognition · Computer Science 2025-09-04 Matthew J. Lynch , Ryan Jacobs , Gabriella Bruno , Priyam Patki , Dane Morgan , Kevin G. Field

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

Computational Engineering, Finance, and Science · Computer Science 2025-06-23 Timbwaoga Aime Judicael Ouermi , Jixian Li , Chris R. Johnson

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…

Computation · Statistics 2014-01-13 Michael McCoy , Joel Tropp

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to…

Image and Video Processing · Electrical Eng. & Systems 2023-06-28 Abu Bucker Siddik , Steven Sandoval , David Voelz , Laura E Boucheron , Luis Varela

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…

Computer Vision and Pattern Recognition · Computer Science 2024-08-06 Nathan Mankovich , Gustau Camps-Valls , Tolga Birdal

Accelerating the design of materials with targeted properties is one of the key materials informatics tasks. The most common approach takes a data-driven motivation, where the underlying knowledge is incorporated in the form of…

Materials Science · Physics 2022-09-28 Shunshun Liu , Kyungtae Lee , Prasanna V. Balachandran

Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use…

Mesoscale and Nanoscale Physics · Physics 2025-11-03 C. J. O. Reichhardt , D. McDermott , C. Reichhardt

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…

Machine Learning · Computer Science 2019-10-16 Takanori Fujiwara , Oh-Hyun Kwon , Kwan-Liu Ma

Previous research on EMA data of mental disorders was mainly focused on multivariate regression-based approaches modeling each individual separately. This paper goes a step further towards exploring the use of non-linear interpretable…

Machine Learning · Computer Science 2022-04-05 Mandani Ntekouli , Gerasimos Spanakis , Lourens Waldorp , Anne Roefs

In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…

Statistics Theory · Mathematics 2020-01-29 Alberto Bernacchia , Philippe Naveau

Purpose: The primary goal of this study is to explore the application of evaluation metrics to different clustering algorithms using the data provided from the Canadian Longitudinal Study (CLSA), focusing on cognitive features. The…

Machine Learning · Computer Science 2025-05-19 ChenNingZhi Sheng