Principal Component Analysis and Quasar Identication Techniques

Principal Component Analysis (PCA) is one of the most common and useful data analysis techniques to perform on a set of observations with variables that may be correlated with one another. PCA can extract the most important relationships in a data set by projecting the data into an orthogonal space where the weighted eigenvectors describe the amount of variance in the data set. These eigenvectors are obtained by the singular value decomposition of the original data set, and are composed of linear coecients which will project the original observables into the new orthogonal space. The linear combinations resulting from this multiplication are called factor scores. The most strongly correlated observables will have factor scores that are largest in magnitude. Although there are several ways to execute PCA, this paper will focus on the PCA of a correlation matrix in order to extract emission line ratios most relevant to the classication