Related papers: Principal component analysis-based inversion of ef…
This tutorial reviews the main steps of the principal component analysis of a multivariate data set and its subsequent dimensional reduction on the grounds of identified dominant principal components. The underlying computations are…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
We develop the variational-cluster-approximation method based on the thermal-pure-quantum-state approach and apply the method to the calculations of the thermodynamic properties of the Hubbard model, thereby obtaining the temperature…
An empirical method of modeling the stellar spectrum of galaxies is proposed, based on two successive applications of Principal Component Analysis (PCA). PCA is first applied to the newly available stellar library STELIB, supplemented by…
Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken…
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…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…
In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…
The temperature of a dust ensemble in a dusty plasma is one of its most fundamental properties. Here, we present experiments using the configurational temperature as a for the temperature analysis in dusty plasmas. Using a model of the…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…
Analytical calculation is presented of the QCD radiative corrections to the rate of the process $b\to c\tau\bar\nu_\tau$ and to the $\tau$ lepton longitudinal polarization in $\tau\bar\nu_\tau$ rest frame. The results are given in the form…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
When inverting solar spectra, image degradation effects that are present in the data are usually approximated or not considered. We develop a data reduction method that takes these issues into account and minimizes the resulting errors. By…
The general context of this study concerns the post-processing of multiline spectropolarimetric observations of stars, and in particular these numerical analysis techniques aiming at the detection and the characterization of polarized…
It has been demonstrated that distillation profiles can be employed to build optimized quarkonium interpolators for spectroscopy calculations in lattice QCD. We test their usefulness for heavy-light systems on (3+1)-flavor ensembles with…
We have executed a survey of nearby, main sequence A, F, and G-type stars with the CHARA Array, successfully measuring the angular diameters of fortyfour stars with an average precision of ~ 1.5%. We present new measures of the bolometric…
A number of empirical correlations that allows us to calculate the effective temperature and surface gravity for a set evolved post-AGB and RV Tauri stars are determined using as calibrators the intrinsic colours of 2MASS (Two Micron All…
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.…
Recently, we developed a method to construct polynomial interatomic potentials from ab-initio calculations in order to accurately describe laser excited solids [PRL 124, 085501 (2020)]. However, ab-initio methods, and therefore analytical…