Generalization Bounds and Uniform Bounds for Multi-Dividing Ontology Algorithms with Convex Ontology Loss Function
Wei Gao, Mohammad Reza Farahani · The Computer Journal · 2017
Ontology, as a useful tool, is widely applied in lots of fields such as geography science, computer science and medical science. Ontology concept similarity calculation is the key part of the algorithms in these applications. A popular trick is to make use of the similarity between vertices on ontology graphs. It relies on an ontology function that maps the vertex set of an ontology graph to real numbers, and multi-dividing is an effective approach to achieve this goal. In this paper, we report the generalization bounds and uniform bounds for kernel-based multi-dividing ontology algorithms, which are stated as regularization schemes. The ontology loss function is convex and meets Lipschitz assumption. The results are obtained in terms of statistical probability inequality and empirical Rademacher complexity.