[ArXiv] component separation methods
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.
Sam Leach:
The main questions that this work did not address are how to deal with pixel-pixel correlated errors in the map, and how to deal with unresolved sources of emission that lead to a type of noise that is correlated between different channels. Naturally there are proposals in the literature based on past experience with the WMAP data.
The fact that we are dealing with continuum emission means that there are often no strong features in the spectra to help with physics identification. Instead the data must be combined with ‘external’ datasets where complementary physics reigns. Then the interpretation proceeds with the use of, for instance, three dimensions models of the Galactic emission. The point I am trying to make is that component separation, to the extent that it is at all possible, it is just a starting point doing astrophysics.
10-01-2009, 3:44 amhlee:
Thanks for your comment. Author’s comments excite me always although I sometimes cannot understand how physical interpretations are deduced and how the external data sets are combined scientifically (or legitimately) from data reduction and analysis process. When I came across your paper, the description of various methodology in the appendix was more valuable to me, which often lacks in other publications. Knowing that astronomy is not statistic, nor computer science, it was something rarely come by. Furthermore, it could motivate people to try various strategies to their data set of statistically similar characteristics.
10-05-2009, 1:05 pm