Stability Analysis of Learning Algorithms for Ontology Similarity Computation

Abstract

Ontology, as a useful tool, is widely applied in lots of areas such as social science, computer science, and medical science. Ontology concept similarity calculation is the key part of the algorithms in these applications. A recent approach is to make use of similarity between vertices on ontology graphs. It is, instead of pairwise computations, based on a function that maps the vertex set of an ontology graph to real numbers. In order to obtain this, the ranking learning problem plays an important and essential role, especially k-partite ranking algorithm, which is suitable for solving some ontology problems. A ranking function is usually used to map the vertices of an ontology graph to numbers and assign ranks of the vertices through their scores. Through studying a training sample, such a function can be learned. It contains a subset of vertices of the ontology graph. A good ranking function means small ranking mistakes and good stability. For ranking algorithms, which are in a well-stable state, we study generalization bounds via some concepts of algorithmic stability. We also find that kernel-based ranking algorithms stated as regularization schemes in reproducing kernel Hilbert spaces satisfy stability conditions and have great generalization abilities.