  The problem of relevance ranking consists of sorting a set of objects with
respect to a given criterion. Since users may prefer different relevance
criteria, the ranking algorithms should be adaptable to the user needs. Two
main approaches exist in literature for the task of learning to rank: 1) a
score function, learned by examples, which evaluates the properties of each
object yielding an absolute relevance value that can be used to order the
objects or 2) a pairwise approach, where a "preference function" is learned
using pairs of objects to define which one has to be ranked first. In this
paper, we present SortNet, an adaptive ranking algorithm which orders objects
using a neural network as a comparator. The neural network training set
provides examples of the desired ordering between pairs of items and it is
constructed by an iterative procedure which, at each iteration, adds the most
informative training examples. Moreover, the comparator adopts a connectionist
architecture that is particularly suited for implementing a preference
function. We also prove that such an architecture has the universal
approximation property and can implement a wide class of functions. Finally,
the proposed algorithm is evaluated on the LETOR dataset showing promising
performances in comparison with other state of the art algorithms.
