Astrophysics Applications of Principal Component Analysis

1. Astrophysics Applications of Principal Component Analysis Zachariah Schrecengost1, ShashiKanbur1 1SUNY Oswego, Oswego, NY • Principal Component Analysis (PCA) • PCA is a way to identify patterns in data and determine how well the data is related • It can be used to compress the data and reduce the number of dimensions with little overall information loss • It is a straight forward procedure, using matrices, that is easily programmable • Previous Method of Analyzing Variable Star and Benefits of Principle Componet Analysis • Fourier Analysis • Requires a large number of parameters • Analysis done on individual stars • Principle Component Analysis • Requires a fewer number of parameters than Fourier • Analysis done on many stars at a time • Process • Rephase raw data from Julian date to phases between 0 and 1 • Interpolate 100 equally spaced points • Normalize rows • Standardize columns • Perform principle component analysis on normalized and standardized data • Applications in Astrophysics • Principle components can be related to various properties of stars (e.g. metallicity, color, etc.) • We have begun to investigate the following relationships. • Period-Luminosity Relation • Results of Multiple Regression: • A0_I = 16.98834-3.08877*logP+0.35815*PC2 • F-Test = 56.588 • Period-Luminosity-Color Relation • Dataset • We analyzed stars from four dataset and constructed plots of principle components 1 and 2 (PC1 and PC2) versus log(period) • OGLE Cepheid stars OGLE RRab stars • OGLE RRc stars RR Lyraes from Kepler Fig. 1: A0 in the I band vs. log(period); red data – observed; black data – regression with period and color; white – regression with period and PC2 Fig. 2: Color vs. Principle Component 2; red data – stars with log(period) < 1; black data – stars with log(period) ≥ 1 References: Kanbur et. al., MNRAS 10 October 2002 Kanbur et. al., MNRAS 27 June 2004 Nemec et. al., MNRAS 01 July 2011 Deb & Singh, Astronomy and Astrophysics 08 August 2011 Murugan, Rukaand ShashiKanbur 2012 Jurcsikand Kovacs 1996 NSF Office of International Science and Engineering award number  1065093