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Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Computational Physics · Physics 2021-08-24 Ziming Liu , Sitian Qian , Yixuan Wang , Yuxuan Yan , Tianyi Yang

Quasar pairs are either physically distinct binary quasars or the result of gravitational lensing. The majority of known pairs are in fact lenses, with a few confirmed as binaries, leaving a population of objects that have not yet been…

Astrophysics · Physics 2009-10-31 Daniel J. Mortlock , Rachel L. Webster , Paul J. Francis

We offer a broad review of Balmer line phenomenology in type 1 active galactic nuclei, briefly sum- marising luminosity and radio loudness effects, and discussing interpretation in terms of nebular physics along the 4D eigenvector 1…

Astrophysics of Galaxies · Physics 2016-02-03 J. W. Sulentic , P. Marziani , A. Del Olmo , S. Zamfir

Understanding the inverse equivalent width - luminosity relationship (Baldwin Effect), the topic of this meeting, requires extracting information on continuum and emission line parameters from samples of AGN. We wish to discover whether,…

Astrophysics · Physics 2007-05-23 Paul J. Francis , Beverley J. Wills

High resolution spectra of quasar absorption systems provide the best constraints on temporal or spatial changes of fundamental constants in the early universe. An important systematic that has never before been quantified concerns model…

Cosmology and Nongalactic Astrophysics · Physics 2021-08-25 Chung-Chi Lee , John K. Webb , Dinko Milaković , Robert F. Carswell

Since their first discovery, quasars have been essential probes of the distant Universe. However, due to our limited knowledge of its nature, predicting the intrinsic quasar continua has bottlenecked their usage. Existing methods of quasar…

Cosmology and Nongalactic Astrophysics · Physics 2024-09-24 Zechang Sun , Yuan-Sen Ting , Zheng Cai

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…

Statistics Theory · Mathematics 2009-11-20 Sungkyu Jung , J. S. Marron

We apply a principal component analysis (PCA) to the spectra of each of the 18 Seyfert 1-like objects observed more than 15 times by the international ultraviolet explorer (IUE) from 1978 until the end of 1991. PCA allows us to decompose…

Astrophysics · Physics 2007-05-23 Marc Turler , Thierry J. -L. Courvoisier

In this paper we report new evidence that measurements of the broad-line widths in quasars are dependent on the source orientation, consistent with the idea that the broad-line region is flattened or disc-like. This reinforces the view…

Astrophysics · Physics 2009-11-11 Matt J. Jarvis , Ross J. McLure

In the context of AGN unification scheme rapid variability properties play an important role in understanding any intrinsic differences between sources in different classes. In this respect any clue based on spectral properties will be very…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-30 Ravi Joshi , Hum Chand , Paul J. Wiita , Alok C. Gupta , Raghunathan Srianand

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…

When an image of a strongly lensed quasar is microlensed, the different components of its spectrum are expected to be differentially magnified owing to the different sizes of the corresponding emitting region. Chromatic changes are expected…

Cosmology and Nongalactic Astrophysics · Physics 2013-06-07 D. Sluse , D. Hutsemékers , F. Courbin , G. Meylan , J. Wambsganss

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Machine Learning · Computer Science 2026-02-05 Thomas Uriot , Elise Chung

We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…

Statistics Theory · Mathematics 2017-04-03 Ilaria Giulini

Further investigation of data on quasars, especially in the ultraviolet band, yields an amazingly coherent narrative which we present in this paper. Quasars are characterised by strong continuum emission and redshifted emission and…

Astrophysics of Galaxies · Physics 2017-12-07 Nimisha G. Kantharia

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Methodology · Statistics 2015-06-16 A. A. Akinduko , A. N. Gorban

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence

We report the results of analysis of the Hbeta emission-line region of a sample of thirty low-redshift (z<1) iron low-ionization broad absorption line quasars (FeLoBALQs). Eleven of these objects are newly classified as FeLoBALQs. A matched…

We measure the spectral properties of a representative sub-sample of 187 quasars, drawn from the Parkes Half-Jansky, Flat-radio-spectrum Sample (PHFS). Quasars with a wide range of rest-frame optical/UV continuum slopes are included in the…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Methodology · Statistics 2024-01-11 Caren Marzban , Ulvi Yurtsever , Michael Richman
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