Relaxation labeling processes are iterative procedures that aim at reducing local ambiguities through a parallel exploitation of contextual information. Recently they have been successfully applied to the problem of word-class disambiguation. In relaxation processes contextual information is embedded in a set of "compatibility coefficients." Several statistical-based interpretations have been given for compatibility coefficients, and recently a new optimization standpoint has been introduced. In this paper we discuss these two approaches for learning compatibilities on the basis of a training sample, and suggest a way to combine them. Experimental results conducted over a sample text are given.