The AstroStat Slog » component separation http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 [ArXiv] component separation methods http://hea-www.harvard.edu/AstroStat/slog/2009/arxiv-component-separation-methods/ http://hea-www.harvard.edu/AstroStat/slog/2009/arxiv-component-separation-methods/#comments Tue, 08 Sep 2009 15:17:34 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/?p=3502 I happened to observe a surge of principle component analysis (PCA) and independent component analysis (ICA) applications in astronomy. The PCA and ICA is used for separating mixed components with some assumptions. For the PCA, the decomposition happens by the assumption that original sources are orthogonal (uncorrelated) and mixed observations are approximated by multivariate normal distribution. For ICA, the assumptions is sources are independent and not gaussian (it grants one source component to be gaussian, though). Such assumptions allow to set dissimilarity measures and algorithms work toward maximize them.

The need of source separation methods in astronomy has led various adaptations of decomposition methods available. It is not difficult to locate those applications from journals of various fields including astronomical journals. However, they are most likely soliciting one dimension reduction method of their choice over others to emphasize that their strategy works better. I rarely come up with a paper which gathered and summarized component separation methods applicable to astronomical data. In that regards, the following paper seems useful to overview methods of reducing dimensionality for astronomers.

[arxiv:0805.0269]
Component separation methods for the Planck mission
S.M.Leach et al.
Check its appendix for method description.

Various library/modules are available through software/data analysis system so that one can try various dimension reduction methods conveniently. The only concern I have is the challenge of interpretation after these computational/mathematical/statistical analysis, how to assign physics interpretation to images/spectra produced by decomposition. I think this is a big open question.

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