Learning to Rank Individuals in Description Logics Using Kernel Perceptrons ⋆ Nicola Fanizzi, Claudia d’Amato, Floriana Esposito Dipartimento di Informatica, Universit` a degli studi di Bari ”Aldo Moro” {fanizzi,claudia.damato,esposito}@di.uniba.it Abstract. We describe a method for learning functions that can predict the rank- ing of resources in knowledge bases expressed in Description Logics. The method relies on a kernelized version of the PERCEPTRON RANKING algorithm which is suitable for batch but also online problems settings. The usage of specific kernel functions that encode the similarity between individuals in the context of knowl- edge bases allows the application of the method to ontologies in the standard representations for the Semantic Web. An extensive experimentation reported in this paper proves the effectiveness of the method at the task of ranking the an- swers to queries, expressed by class descriptions when applied to real ontologies describing simple and complex domains. 1 Introduction Ranking a set of individual objects, as the result of relations sought between them and their relative relevance, is a fundamental task with a plenty of applications. Typically, ranked resources (e.g. documents, web services) may be returned as a result of retrieval process (from a corpus, a database, a directory, etc.). When the relevance of the out- comes depends exclusively on the query specification, this task is quite well-understood and many effective solutions exist, even for approximate cases. However, the problem likely turns out to be much harder when a general and precise measure of the relevance of the results is too complex or unavailable (e.g. multiple relevance orders, subjective user-dependent preferences, etc.). Essentially, based on a request (a query) and, possibly, on some previous partial indications of an intended relevance (e.g. some feedback from the user), the set of re- trieved resources must be ordered according to such indications. It may be possible to (partially) elicit the required information exploiting imprecise criteria that can often be expressed by means of examples rather than in a general and formal way. A related pro- cess of result ranking based on relevance-feedback mechanisms is represented by the task known as collaborative filtering which aims at detecting the relevance of informa- tion items for new users based on rankings previously acquired from others. All such problems can be cast in the framework of inductive learning from examples [9]. Given previously rated instances (e.g. movies, songs, etc.), the aim is to induce a hypothesis ⋆ This work was partially funded by the MBLab FAR Project (MIUR DM19410). A short ver- sion of this paper has been accepted to ECAI2010 [6].