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Principal Component Analysis in Astrophysics

Principal Component Analysis in Astrophysics. Carolina Ödman SKA – SAAO - AIMS. Principal Component Analysis. Origin: <data>. How does PCA work?. Correlated data. How does PCA work?. De-correlated data. Eigenvalues. Eigenvectors. How does PCA work?. 1 st eigenvalue

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Principal Component Analysis in Astrophysics

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  1. Principal Component Analysisin Astrophysics Carolina Ödman SKA – SAAO - AIMS

  2. Principal Component Analysis Origin:<data>

  3. How does PCA work? Correlated data

  4. How does PCA work? De-correlated data Eigenvalues Eigenvectors

  5. How does PCA work? 1st eigenvalue Strongest correlation Direction given by 1st eigenvector • De-correlation • Extraction of trends • Data compression

  6. Example

  7. PCA on 100,000 stellar spectra from SDSS McGurk, Kimball & Ivezíc 2010 - aXiv:1001.4340v2

  8. Supernovae Classification Newling et al 2010 - arXiv:1010.1005v1 see poster

  9. Eigen-lightcurves Project SNe Ia & non-Ia on eigen-lightcurves  rapid classifier?

  10. Non-linear correlations Red: Ωb = 0.0462, ΩCDM = 0.2538, ΩΛ=0.7, H0=70 Blue: Ωb = 0.1462, ΩCDM = 0.1538, ΩΛ=0.7, H0=70 Green: Ωb = 0.0462, ΩCDM = 0.1538, ΩΛ=0.8, H0=70

  11. Non-linear PCA • Auto-associative neural networks • Principal curves and manifolds • Kernel approaches

  12. Conclusions • We are interested in Non-linear PCA because we think the method can • help extract complex correlations between • cosmological parameters • help develop new classifiers • help understand systematics that leave non- • linear signatures in raw data

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