SOMBI: Bayesian identification of parameter relations in unstructured
  cosmological data
  This work describes the implementation and application of a correlation
determination method based on Self Organizing Maps and Bayesian Inference
(SOMBI). SOMBI aims to automatically identify relations between different
observed parameters in unstructured cosmological or astrophysical surveys by
automatically identifying data clusters in high-dimensional datasets via the
Self Organizing Map neural network algorithm. Parameter relations are then
revealed by means of a Bayesian inference within respective identified data
clusters. Specifically such relations are assumed to be parametrized as a
polynomial of unknown order. The Bayesian approach results in a posterior
probability distribution function for respective polynomial coefficients. To
decide which polynomial order suffices to describe correlation structures in
data, we include a method for model selection, the Bayesian Information
Criterion, to the analysis. The performance of the SOMBI algorithm is tested
with mock data. As illustration we also provide applications of our method to
cosmological data. In particular, we present results of a correlation analysis
between galaxy and AGN properties provided by the SDSS catalog with the cosmic
large-scale-structure (LSS). The results indicate that the combined galaxy and
LSS dataset indeed is clustered into several sub-samples of data with different
average properties (for example different stellar masses or web-type
classifications). The majority of data clusters appear to have a similar
correlation structure between galaxy properties and the LSS. In particular we
revealed a positive and linear dependency between the stellar mass, the
absolute magnitude and the color of a galaxy with the corresponding cosmic
density field. A remaining subset of data shows inverted correlations, which
might be an artifact of non-linear redshift distortions.
