Characteristics of Optimal Function for Ontology Similarity Measure via Multi-dividing

As a powerful tool, ontology has been widely applied in social science, medicine science and computer science. In computer networks, especially, ontology is used for search extension, thus boost the quality of information retrieval. Ontology concept similarity calculation is an essential problem in these applications. A new method to get similarity between vertices on ontology graph is by machine learning, and multi-dividing algorithm is suitable for ontology problem. It is usually get an ontology function which maps the vertices of ontology graph to real numbers. Such function is given by learning a training sample which contains a subset of vertices of ontology graph. In this paper, we study the properties of best ontology function for this method. Some results under different loss functions are given.