Analogical Dissimilarity: definition, algorithms and first experiments in machine learning

This paper defines the notion of analogical dissimilarity between four objects, with a special focus on dissimilarity between objects structured as sequences. Firstly, it studies the case where the four objects have a null analogical dissimilarity, i.e. are in an analogical relation. Secondly, when one of these objects is unknown, it gives algorithms to compute it. In particular, it studies a new formulation of solving analogical equations on sequences, based on the edit distance between strings. Thirdly, it tackles the problem of defining analogical dissimilarity, which is a measure of how close four objects are from being in analogical relation. To finish, it gives learning algorithms, i.e. methods to find the triple of objects in a learning sample which has the least analogical dissimilarity with a given object