Algorithm of Ontology Similarity Measure Based on Similarity Kernel Learning

Ontology, as a structured conceptual model of knowledge representation and storage, has widely been used in biomedical and pharmaceutical research. The nature of the ontology application is to get the similarity between ontology vertices, and thus reveal the similarity of their corresponding concepts and intrinsic relationships. The similarity for all pairs of vertices forms a similarity matrix of ontology, and the aim of ontology algorithm is to obtain the optimal similarity matrix. In this paper, we propose a new algorithm to get a similarity matrix in terms of learning the optimal similarity kernel function for ontology. The simulation experiment is designed for biology “Go” ontology application


INTRODUCTION
In computer science, ontology is a model for knowledge storing and representation, and has been applied in image retrieval, knowledge management, information retrieval search extension, information systems, collaboration, and intelligent information integration. In recent years, as an effective concept semantic model, ontology has been widely employed in medical science, pharmacology science and biology science (for instance, see [1][2][3]).
Each vertex on an ontology graph represents a concept; each edge on an ontology graph represents a connection between two concepts. Let G be a simple undirected graph correspond to ontology O, the goal of ontology application is similarity measuring between ontology vertices, and the aim of similarity measure is to approach a similarity function which maps each pair of vertices to a non-negative real number.
In biology and pharmacy science, we use a vector to represent the information for each gene or disease. By studying the similarity of corresponding information between the genes, or the similarity of corresponding information between gene and diseases, we study the linkages between different genes, and what types of genes cause the certain disease.
There are some effective technologies for getting efficient ontology similarity measure algorithm. [4] first proposed that ranking method can be employed in ontology similarity calculation. [5] raised fast ontology algorithm in order to reduce the time complexity of the algorithm. [6] argued that ontology function can be given by optimizing NDCG [7] obtained the ontology function in terms of the regression measure, and applied such idea in physics education. approach. In [8] the proposal was getting ontology function based on half transductive ranking. [9] explored the learning theory approach for ontology similarity computation in a setting when the ontology graph is a tree. In view of the multi-dividing algorithm in which the vertices divided into k parts correspond to the k classes of rates. The rate values of all classes are decided by experts. Then, a vertex in a rate a has larger value than any vertex in rate b (where 1  a< b  k) under ontology function f. Finally, the similarity between two ontology vertices is measured by the difference of two real numbers which they correspond to. Thus, the multi-dividing algorithm is reasonable to learn a score function for an ontology graph with a tree structure. [10] proposed new criterion for multi-dividing ontology algorithm from AUC standpoint, which was designed to avoid the choice of loss function. [11] presented new algorithms for ontology similarity measurement and ontology mapping by virtue of harmonic analysis and diffusion regularization on hypergraph. Recently, [12]proposed new algorithms for ontology similarity measurement such that the new computational models consider operational cost in the real implement.
Several papers have contributed to the theoretical analysis for different ontology settings. [13] have studied the uniform stability of multi-dividing ontology algorithm and gave the generalization bounds for stable multi-dividing ontology algorithms. [14] researched the strong and weak stability of multi-dividing ontology algorithm. [15] learned some characteristics for such ontology algorithm. [16] studied the multi-dividing ontology algorithm from a theoretical view. It is highlighted that empirical multi-dividing ontology model can be expressed as conditional linear statistical, and an approximation result is achieved based on projection method. [17] presented the characteristics of best ontology score function among piece constant ontology score functions. [18] investigated the upper bound and the lower bound minimax learning rate which is obtained based on low noise assumptions. [19] and [20] presented an approach of piecewise constant function approximation for AUC criterion multi-dividing ontology algorithms.
Since the similarity of all pairs of vertices forms a similarity matrix, the aim of ontology application boils down to derive the optimal similarity matrix. In this paper, we focus on the ontology algorithm to deduce the best similarity matrix by learning the similarity kernel. The organization of this paper is as follows: the ontology problem and notations for basic setting are showed in Section 2; the computing model and basic ideals are stated in Section 3; in Section 4, an simulation experiment is designed to test the efficiency of the algorithm, and the data result reveal that our algorithm has high precision ratio for biology application.

Setting and Notation
For each vV, we use a vector to express all the information of v in ontology graph. The elements in V are drawn independently and randomly according to some unknown distribution D. Without causing confusion, we use v to represent the vertex and the information vector corresponds to v. Given a training set S= {v1,… vm}  V with size m, the aim of ontology learning algorithms is to get an optimal similarity function Sim * : V  V    . Since the posicite kernel function K:  also return a non-negative real number for each pair of ontology vertices, we consider similarity kernel instead of similarity function. In this article, we determine the similarity between vertices via learning optimal similarity kernel function.
Recall that the feature mapping  : where v E is the expected value of  and vertex v is drawn from the distribution D. Kernel function K: V V    is a positive definite symmetric (PDS) function which consists of information of feature mapping  associated to K. For each pair of v, v′  V, the centered kernel Kc associated to K is expressed by The definition doesn"t rely on the selecting of the feature mapping associated to K. Note that Kc is also a PDS kernel since Tr( )

Similarity Kernel Learning for Ontology Algorithm
In this section, we consider our ontology algorithms via learning kernels in the form of linear combinations of p base kernels Kk, where k [1, p]. In such situation, the final hypothesis learned belongs to the reproducing kernel Hilbert space Notice that in order to guarantee K is a PDS kernel, the mixture weights are choice subject to the condition   0 and  =  >0 is a regularization parameter. Our algorithm is to determine the mixture weights  . W.l.o.g., we assume that the centered base kernel matrices c k K are independent. Hence, we infer

Simulation Experiment
In this section, we design the following simulation experiment concerning ontology similarity measures. We use biology ontology O1 which was constructed in http://www. geneontology.org. Fig. 1 shows the basic structure of O1. P@ N (Precision Ratio, see [21] for more detail) is used to quantify the quality of our experiment. First, we obtain the closest N concepts for every vertex on the "GO" ontology graph by biology expert, and then we obtain the first N concepts for every vertex on ontology graph by the algorithm and compute the precision ratio. At the same time, we apply ontology method in [8], and [22] to the "GO" ontology. We calculate the accuracy by these two algorithms and compare the result to algorithm proposed in our paper, part of the data refer to Tab.1.  By the experiment data presented in Tab. 1, we arrived at the conclusion that our algorithm is more efficiently than algorithms raised in [8], and [22] especially when N is large enough. Therefore, this new ontology similarity algorithm by virtue of centered kernel learning has high efficiency.

Summary
Ontology, as a data representation model, has been widely used in medical science, pharmacology science and biology science. And, it is proved to be highly efficient. In our paper, we apply the tricks of kernel learning to design the new similarity measure algorithms for ontology. The new algorithms have high quality according to the simulation data presented in the former section. This technology contributes to the state of art for ontology in biology and pharmacology applications.