Introduction to Principal Components Analysis

TL;DR

This paper introduces Principal Components Analysis (PCA) as a method to analyze correlations among spectral parameters in AGN, aiming to uncover underlying physical relationships and insights.

Contribution

It explains the purpose, principles, and interpretation of PCA in the context of QSO spectroscopy, illustrating its application to AGN data analysis.

Findings

PCA helps identify correlated spectral parameters.

Application to QSO spectra reveals potential physical relationships.

PCA can uncover new insights into AGN properties.

Abstract

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, and how, different subsets of measured parameters may correlate with each other. This general problem is the domain of Principal Components Analysis (PCA). We discuss the purpose, principles, and the interpretation of PCA, using some examples from QSO spectroscopy. The hope is that identification of relationships among subsets of correlated variables may lead to new physical insight.