Related papers: Quasar Main Sequence: a line or a plane?

By observing the high galactic latitude equatorial sky in drift scan mode with the QUEST (QUasar Equatorial Survey Team) Phase 1 camera, multi-bandpass photometry on a large strip of sky, resolved over a large range of time scales (from…

Based on a new sample of 355 quasars with significant optical polarization and using complementary statistical methods, we confirm that quasar polarization vectors are not randomly oriented over the sky with a probability often in excess of…

We present a new and simple technique for selecting extensive, complete and pure quasar samples, based on their intrinsic variability. We parametrize the single-band variability by a power-law model for the light-curve structure function,…

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

Highly accreting quasars are characterized by distinguishing properties in the 4D eigenvector 1 parameter space that make them easily recognizable over a broad range range of redshift and luminosity. The 4D eigenvector 1 approach allows us…

The broad emission lines commonly seen in quasar spectra have velocity widths of a few per cent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Quasars accreting matter at very high rates (known as extreme Population A [xA] quasars, possibly associated with super-Eddington accreting massive black holes) may provide a new class of distance indicators covering cosmic epochs from…

A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…

We introduce Adaptive Subspace PCA (AS-PCA), a framework for principal component analysis of random elements in a general separable Hilbert space. AS-PCA projects the covariance operator onto a data-adaptive finite-dimensional subspace…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

From a Principal Component Analysis (PCA) of 78 z~3 high quality quasar spectra in the SDSS-DR7, we derive the principal components characterizing the QSO continuum over the full wavelength range available. The shape of the mean continuum,…

We report on the results of a new spectroscopic monitoring campaign of the quasar PG 0026+129 at the Calar Alto Observatory 2.2m telescope from July 2017 to February 2020. Significant variations in the fluxes of the continuum and…

We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by…

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…

Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a third-order generalization of principal component analysis (PCA), its solution of searching for the locally maximum skewness…

Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…