Supervised learning of preference relations
In this paper we investigate the problem of learning a prefer ence relation from a given set of ranked objects. The main difference between preference learning a nd standard classification learning is the demand, that the mapping from objects to ranks has to be transitive and ant isymmetric. To model this problem we present an approach that performs a linear mapping from objects to scal ar utility values and thus guarantees transitivity and antisymmetry. The learning of the preference between objec ts is formulated as a classification problem on pairs of objects and is solved using the principle of structural ri sk minimization. The approach is extended to nonlinear utility functions by using the potential function method (t he so called kernel trick), which allows to incorporate higher order correlations of features into the utility func tion at minimal computational costs.