1 / 12

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

cricket
Download Presentation

Principal Component Analysis in Astrophysics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related