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Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

We apply Principal Component Analysis (PCA) to study the variability of the X-ray continuum in the Seyfert 1 galaxy NGC 7469. The PCA technique is used to separate out linear components contributing to variability between multiple datasets;…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

We describe and summarize the findings from our CCD time-series photometry of globular clusters (GCs) program and the use of difference image analysis (DIA) in the extraction of very precise light curves even in the crowded central regions…

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…

The primary goal of this paper is to derive precise Fourier parameters of the radial velocity (RV) curves for fundamental and first-overtone Galactic Cepheids. For each star, we carefully selected RV measurements available in the literature…

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event…

Model-independent analysis (MIA) methods are generally useful for analysing complex systems in which relationships between the observables are non-trivial and noise is present. Principle Component Analysis (PCA) is one of MIA methods…

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…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

We demonstrate the use of a variant of Principal Component Analysis (PCA) for discrimination problems in astronomy. This variant of PCA is shown to provide the best linear discrimination between data classes. As a test case, we present the…

Fourier decomposition is a well established technique used in stellar pulsation. However the quality of reconstructed light curves using this method is reduced when the observed data have uneven phase coverage. We use simulated annealing…

RR~Lyrae variables are widely used tracers of Galactic halo structure and kinematics, but they can also serve to constrain the distribution of the old stellar population in the Galactic bulge. With the aim of improving their near-infrared…

This paper aims to develop the first method to reconstruct the shape of the RV curves of short-period fundamental-mode Cepheids, based exclusively on their pulsation period and the morphology of their $V$-band light curves (LCs). We…

We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…