Piecewise function approximation and vertex partitioning schemes for multi-dividing ontology algorithm in AUC criterion setting (I)

Abstract

Ontology is a useful tool with wide applications in various fields and attracts widespread attention of scholars, and ontology concept similarity calculation is an essential problem in these application algorithms. An effective method to get similarity between vertices on ontology is based on a function, which maps ontology graph into a line and maps each vertex in graph into a real-value, and the similarity is measured by the difference of their corresponding scores. The area under the receiver operating characteristics curve (AUC) criterion multi-dividing method is suitable for ontology problem. In this paper, we present piecewise constant function approximation approach for AUC criterion multi-dividing ontology algorithm and focus on vertex partitioning schemes. Using the techniques of statistical learning theory, theoretical characteristics of the approximation algorithm are provided with partitioning schemes, and a splitting rule is designed for vertex partitioning.