Learning rate of gradient descent multi-dividing ontology algorithm

As acknowledge representation model, ontology has wide applications in information retrieval and other disciplines. Ontology concept similarity calculation is a key issue in these applications. One approach for ontology application is to learn an optimal ontology score function which maps each vertex in graph into a real-value. And the similarity between vertices is measured by the difference of their corresponding scores. The multi-dividing ontology algorithm is an ontology learning trick such that the model divides ontology vertices into k parts correspond to the k classes of rates. In this paper, we propose the gradient descent multi-dividing ontology algorithm based on iterative gradient computation and yield the learning rates with general convex losses by virtue of the suitable step size and regularisation parameter selection.