Astrophysics Applications of Principal Component Analysis Zachariah Schrecengost 1 , Shashi Kanbur 1 1 SUNY Oswego, Oswego, NY NSF Office of International Science and Engineering award number 1065093 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, Ruka and Shashi Kanbur 2012 Jurcsik and Kovacs 1996 Principal Component Analysis (PCA) o PCA is a way to identify patterns in data and determine how well the data is related o It can be used to compress the data and reduce the number of dimensions with little overall information loss o It is a straight forward procedure, using matrices, that is easily programmable Previous Method of Analyzing Variable Star and Benefits of Principle Componet Analysis o Fourier Analysis o Requires a large number of parameters o Analysis done on individual stars o Principle Component Analysis o Requires a fewer number of parameters than Fourier o Analysis done on many stars at a time Process o Rephase raw data from Julian date to phases between 0 and 1 o Interpolate 100 equally spaced points o Normalize rows o Standardize columns o Perform principle component analysis on normalized and standardized data 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 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. o Period-Luminosity Relation Results of Multiple Regression: A0_I = 16.98834- 3.08877*logP+0.35815*PC2 F-Test = 56.588 o Period-Luminosity-Color Relation 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

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Astrophysics Applications of Principal Component Analysis. Zachariah Schrecengost 1 , Shashi Kanbur 1 1 SUNY Oswego, Oswego, NY. Principal Component Analysis ( PCA ) PCA is a way to identify patterns in data and determine how well the data is related - PowerPoint PPT Presentation

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Page 1: Astrophysics Applications of Principal Component Analysis

Astrophysics Applications of Principal Component AnalysisZachariah Schrecengost1, Shashi Kanbur1

1SUNY Oswego, Oswego, NY

NSF Office of International Science and Engineering award number 1065093

References:Kanbur et. al., MNRAS 10 October 2002Kanbur et. al., MNRAS 27 June 2004Nemec et. al., MNRAS 01 July 2011Deb & Singh, Astronomy and Astrophysics 08 August 2011Murugan, Ruka and Shashi Kanbur 2012Jurcsik and Kovacs 1996

Principal Component Analysis (PCA)

o PCA is a way to identify patterns in data and determine how well the data is related

o It can be used to compress the data and reduce the number of dimensions with little overall information loss

o It is a straight forward procedure, using matrices, that is easily programmable

Previous Method of Analyzing Variable Star and Benefits of Principle Componet Analysis

o Fourier Analysis

o Requires a large number of parameterso Analysis done on individual stars

o Principle Component Analysis

o Requires a fewer number of parameters than Fourier

o Analysis done on many stars at a time

Processo Rephase raw data from Julian date to phases between 0

and 1o Interpolate 100 equally spaced pointso Normalize rows

o Standardize columns

o Perform principle component analysis on normalized and standardized data

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

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.o Period-Luminosity RelationResults of Multiple Regression:A0_I = 16.98834-3.08877*logP+0.35815*PC2F-Test = 56.588

o Period-Luminosity-Color Relation

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