An optimal basis system for cosmology: data analysis and new
  parameterisation
  We define an optimal basis system into which cosmological observables can be
decomposed. The basis system can be optimised for a specific cosmological model
or for an ensemble of models, even if based on drastically different physical
assumptions. The projection coefficients derived from this basis system, the
so-called features, provide a common parameterisation for studying and
comparing different cosmological models independently of their physical
construction. They can be used to directly compare different cosmologies and
study their degeneracies in terms of a simple metric separation. This is a very
convenient approach, since only very few realisations have to be computed, in
contrast to Markov-Chain Monte Carlo methods. Finally, the proposed basis
system can be applied to reconstruct the Hubble expansion rate from supernova
luminosity distance data with the advantage of being sensitive to possible
unexpected features in the data set. We test the method both on mock catalogues
and on the SuperNova Legacy Survey data set.
