IV. applies Degree Centrality, Betweenness Centrality, and Eigenvector Centrality

IV. Ontology Summarization Techniques Ontology summarization is usually considered as an effective way to understand an ontology in order to support different tasks such as ontology reusing in ontology construction development. In literatures, ontology summarization is referred to extractive summarization approach in which the important concepts (at the schema layer) and important entities (at the data layer) are extracted and represented as a summary of an ontology. Based on different measurements in the section III, various methods in ontology summarization have been proposed which are highlighting different criterias to generate a summary for an ontology. In the next section, we are primarily focusing on the approaches which are dedicated in Ontology Summarization and providing more details about them. Additionally, Table I represents an overview of the models, the measures and the expected outcome for each model. A. RDF sentence based approach In 9, 31, an RDF sentence is considered as a basic building block in generating ontology summary. The proposed model consists of four main components including RDF sentence Builder, Graph Builder, Salience Assessor, and Re-ranker. The key point in this approach is that the user preference will be discussed to determine the weight of links between RDF sentences. In fact, from RDF sentence Builder and Graph Builder components the ontology is mapped to a set of RDF sentences and an RDF Sentence Graph is build based on set of RDF sentences and user’s preference. The Salience Assessor component is responsible to do link analysis on RDF Sentence Graph, generated from the previous component, in order to assess the salience of RDF sentences. This component applies Degree Centrality, Betweenness Centrality, and Eigenvector Centrality to assess the RDF sentences and finally, rank them according to their salience. Re-ranker component in the last step generate the final summary of the ontology. The coherence of the summary and its coverage on the original ontology are also considered in this section in addition to user-specified salient RDF sentences. To evaluate the proposed approach the authors used Kendall’s tau Statistic 40 to measure the agreement between the model’s output and human generated results. B. Personalized Ontology Summary Queiroz-Sousa et al. 30 defines two steps in ontology summarization including finding key concepts and select them to generate a summary. For the first step, identifying key concepts, they introduce relevance measurement which is inspired from two main measurements including Degree Centrality and Closeness Centrality (equation 20). relevance(C) = ? ? DC(C) + ? ? CC(C) (20) Where ? + ? = 1. In the second step, they develop Broaden Relevant Paths (BRP) algorithm in order to find the best path within an ontology that represents a set of interrelated vertices with higher relevance. The BRP algorithm aims to generate three lists including PathSet, NodeSet, and AdjacentNodes. The PathSet list stores the best paths generated by the algorithm. The quality of each path is defined through two metrics including Relevance Coverage and Relevance Degree. The Relevance Coverage is determined by the proportion of the sum of vertices’ relevance within a path by the sum of relevance of the vertices with in the original graph. Relevance Degree assesses the relevance average within a path by the higher value of relevance in the graph. The NodeSet covers all vertices ordered by their relevance values and the AdjacentNodes includes the vertices that have relationships with the vertices of paths contained in the PathSet. The AdjacentNodes arrange the vertices based on Relation Relevance score and the Relation Relevance is a function of the number of relationships among a vertex and the paths contained in PathSet, the sum of relevance values of that vertex in a particular path over the number of vertices contained in the PathSet list, and finally, the relevance of that vertex. The ultimate summary in this approach containing the most relevant concepts with respect to all relationships between those concepts while considering the parameters set by the user. C. Ontology-Based Schemas in PDMS In Pires et al. 25 model, degree centrality and frequency measurements are two key points to generate a summary for an ontology. They have applied the extended version of degree centrality in which the type of relationships between concepts are considered in addition to number of relations that each concept has. The frequency measure of each concept in this model also determines the importance of each concept and the combination of two measurements is define as relevance score of that concept. relevance(C) = ?.DC(C) + ? ? Fr(C) (21) Where ? + ? = 1. The relevance score of each concept needs to be greater than or equal to relevance score threshold to be considered as a good candidate for the final summary. Finding group adjacent relevant concepts and identifying paths between those groups of concepts are two phases after assigning a relevance score to each concept. D. Ontology Summarization: An Analysis and An Evaluation Li et al. 28, highlights the lack of consensus in ontology summarization area and try to come up with a generalized approach for ontology summarization while focusing more on facilitating user understanding of ontology using a few space as possible. They mainly concentrate on linguistic and structural aspects on ontology as the primary features to be looked in ontology summarization. In light of linguistic aspects, popularity and name simplicity are two criteria to be discussed and density and reference are two other criteria that need to be considered with respect to structural aspects on ontology. For their evaluation they used Kendall’s tau Statistic 40 which is often applied to calculate the agreements between two measured quantities.

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