Learning Non-linear Transform with Discrim- Inative and Minimum Information Loss Priors

This paper proposes learning a non-linear transform with two priors. The first is a discriminative prior defined using a measures on a support intersection and the second is a minimum information loss prior expressed as a constraint on the conditioning and the coherence. An approximation of the measures for the discriminative prior is addressed, connecting it to a similarity concentrations. Along quantifying the discriminative properties of the transform representation a sensitivity analysis of the similarity concentration w.r.t. the parameters of the nonlinear transform is given. Furthermore, a measure, related to the similarity concentration, reflecting the discriminative properties, named as discrimination power is introduced and its bounds are presented. To support and validate the theoretical analysis a learning algorithm with the proposed prior is presented. The advantages and the potential of the proposed algorithm are evaluated by a computer simulation.