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As a conceptual semantic tool, ontology is widely used in many disciplines such as genetics, nutrition, and social sciences. The key issues for ontology applications are similarity calculations and ontology alignment. In recent years, various machine learning methods and computational models have been widely used in ontology optimization and computation. The core idea is to map the entire ontology graph into one-dimensional data, such as on a real axis or on a natural number set. Through the analysis of the previous multi-dividing ontology algorithm, the technique of achieving dimensionality reduction comes from the pairwise comparison of the ontology sample vertices. The weakness of such tricks is that only two ontology vertices can be extracted for comparison at a time, which causes the number of vertex pairs to be compared in the optimization model to become very large as the totally ontology sample size increases. This paper proposes a new class of ontology learning strategies, which aims to arrange the ontology concepts into one-dimensional data according to the sequence of natural numbers. The ontology optimization model does not compare two ontology vertices, but compares a set of ontology vertices and calculates the weight of each vertex by means of random walk calculating. Each set of compared ontology vertices constitutes a hyperedge, and thus the ontology sample sets and the computational framework are represented by hypergraph and its associated bipartite graph. The algorithm proposed in this paper has potential guiding significance and theoretical value for engineering applications. In addition, two examples are presented to illustrate that our hypergraph based ontology learning algorithm is effective for a specific application background.

Abstract In the past ten years, researchers have always attached great importance to the application of ontology to its relevant specific fields. At the same time, applying learning algorithms to many ontology algorithms is also a hot topic. For example, ontology learning technology and knowledge are used in the field of semantic retrieval and machine translation. The field of discovery and information systems can also be integrated with ontology learning techniques. Among several ontology learning tricks, multi-dividing ontology learning is the most popular one which proved to be in high efficiency for the similarity calculation of tree structure ontology. In this work, we study the multi-dividing ontology learning algorithm from the mathematical point of view, and an approximation conclusion is presented under the linear representation assumption. The theoretical result obtained here has constructive meaning for the similarity calculation and concrete engineering applications of tree-shaped ontologies. Finally, linear combination multi-dividing ontology learning is applied to university ontologies and mathematical ontologies, and the experimental results imply that the higher efficiency of the proposed approach in actual applications.

Ontology is one of the oldest terminologies in physics and is used to describe the origin and most essential attributes of all things in the world. With the development of contemporary science, ontology was given a specific definition and then introduced into the computer science as a conceptual model to describe the relationship between objects. In the past decade, the algorithms and applications in the ontology-related field have attracted the attention of many scholars. In this work, a support vector machines based multi-dividing ontology learning algorithm is proposed. We pay attention to the similarity of topological indices in chemical graph theory, and apply SVM-based multi-dividing ontology learning algorithms to give some calculation results of similarity between topological indices.

In biology field, the ontology application relates to a large amount of genetic information and chemical information of molecular structure, which makes knowledge of ontology concepts convey much information. Therefore, in mathematical notation, the dimension of vector which corresponds to the ontology concept is often very large, and thus improves the higher requirements of ontology algorithm. Under this background, we consider the designing of ontology sparse vector algorithm and application in biology. In this paper, using knowledge of marginal likelihood and marginal distribution, the optimized strategy of marginal based ontology sparse vector learning algorithm is presented. Finally, the new algorithm is applied to gene ontology and plant ontology to verify its efficiency.

The ontology sparse vector learning algorithm is essentially a dimensionality reduction trick, i.e., the key components in the p-dimensional vector are taken out, and the remaining components are set to zero, so as to obtain the key information in a certain ontology application background. In the early stage of ontology data processing, the goal of the algorithm is to find the location of key components through the learning of some ontology sample points, if the relevant concepts and structure information of each ontology vertex with p-dimensional vectors are expressed. The ontology sparse vector itself contains a certain structure, such as the symmetry between components and the binding relationship between certain components, and the algorithm can also be used to dig out the correlation and decisive components between the components. In this paper, the graph structure is used to express these components and their interrelationships, and the optimal solution is obtained by using spectral graph theory and graph optimization techniques. The essence of the proposed ontology learning algorithm is to find the decisive vertices in the graph Gβ. Finally, two experiments show that the given ontology learning algorithm is effective in similarity calculation and ontology mapping in some specific engineering fields.

Ontology, a common tool in various fields of natural sciences, aims to get the optimal ontology similarity calculation function. Favored by researchers from semantic query and other disciplines, it is used to calculate the similarity between ontology concepts. The semantic information of each concept is expressed by a d-dimensional vector, and the similarity calculation is transformed into the geometric distance calculation of the two corresponding vectors. Using the Mahalanobis distance calculation formula, the ontology algorithm can contribute to getting the optimal distance matrix. In this paper, in terms of the coordinate descent trick and iterative method, we get the ontology distance matrix learning algorithm, and then apply it to ontology similarity computation and ontology mapping. Moreover, the ontology distance matrix learning approach in the manifold setting is discussed, and its kernel solution is studied as well. The main ontology learning algorithm is illustrated by a comparison of other ontology algorithmic data in a specific application context. [ABSTRACT FROM AUTHOR]

In order to represent the semantics and concepts better, the ontology, as an efficient model, has penetrated into all research areas of the computer science and information technology. In recent years, the ontology framework has also been applied to biology, chemistry, pharmaceutics, geography, and other fields, and it has attracted much attention from the researchers. Multi-dividing ontology algorithm is one of the popular learning approaches for ontology applications in which the vertex set and sample data are divided into several parts. In this paper, we introduce a new ontology optimization scheming by means of representer theorem and kernel function, and the method is a kind of linear programming. Four experiments are designed for the application of ontology algorithms in different fields to test the effectiveness by comparing the implement data. [ABSTRACT FROM AUTHOR]

In recent years, the ontology problem has gained attention in machine learning and it has many applications in various fields. Ontology similarity computation plays a critical role in practical implementations. In ontology learning setting, one learns a real-valued score function that assigns scores to ontology vertices. Then, the similarity between vertices is weighted in terms of the difference between their corresponding scores. The purpose of this paper is to report a new ontology learning algorithm for ontology similarity measuring and ontology mapping by means of magnitude preserving. The classes of ontology loss function are considered in regularization ontology framework, the ontology function is supposed to be linear, and the gradient descent implement is presented for getting the optimal ontology function. The result data from our four simulation experiments imply that the new proposed ontology trick has high efficiency and accuracy in biology and plant science with regard to ontology similarity measure, and humanoid robotics and education science with regard to ontology mapping. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the field of information retrieval, ontology acts as an effective way to search the information that has highly semantic similarity of the original query concept, and return the results to the user. The relationship between different ontologies is created through ontology mapping, the essence of which is similarity computation. In this article, we present the sparse vector algorithms for ontology similarity measure and ontology mapping in terms of optimization frameworks. Proximal operator and proximal dividing technologies are used to determine the optimal solution. The simulation experimental results show that the new proposed algorithms have high efficiency and accuracy on ontology similarity measure and ontology mapping in multiple disciplines. [ABSTRACT FROM AUTHOR]

Ontology, as a useful tool, has been widely applied in various fields, and ontology concept similarity calculation is an essential problem in these application algorithms. A recent method to get similarity between vertices on ontology is not by pairwise computation but based on a function which maps ontology graph into a line and maps every vertex in graph into a real-value, the similarity is measured by the difference of their corresponding scores. The multi-dividing method is suitable for ontology problem and plays a key role in achieving this. Such ontology function is given by learning a training sample which contains a subset of vertices with k classes from ontology graph. In this paper, we propose a new multi-dividing ontology algorithm framework, which is designed to avoid the choice of loss function. Meanwhile, there is such a vertex selection policy in new multi-dividing ontology algorithm that it guarantees that the new algorithm can be employed for an ontology graph with its structure rather than a tree. We provide some theoretical characteristics of the new multi-dividing ontology algorithm, and show that the new algorithm is convergent. [ABSTRACT FROM AUTHOR]

In recent years, many learning technologies have been applied in ontology similarity measuring and ontology mapping via learning an ontology function f : V → R which maps an ontology graph to the real line. In these settings, all the information for an ontology vertex (corresponding to concept) is expressed as a vector. However, in a special application, the value of ontology function for each ontology vertex is determined by a few components of the vector. The aim of feature extraction for ontology vector is to obtain these components to fix the index set of the vector, and such a procedure is equivalent to learning an ontology sparse vector in which most components are zero. In this paper, we raise an ontology sparse vector learning model for ontology similarity measuring and ontology mapping in terms of SOCP. The balance term consists of Ω norm, and the directed acyclic graph is employed in ontology setting for backward and forward procedure. Then, the active index set algorithm is designed to moderate the value of p, thus applications will be extended. Finally, five experiments are presented on various fields to verify the efficiency of the new ontology algorithm for ontology similarity measuring and ontology mapping in multidisciplinary research. [ABSTRACT FROM AUTHOR]

Along with the arrival of the era of large amount of data, many machine learning methods have been applied to the ontology similarity calculation and ontology mapping. In this paper, we raise an infinite push model for ontology similarity measuring and ontology mapping in multi-dividing setting. The iterative algorithm and generalization bound are given by virtue of the dual solution for optimization and the trick of covering number approach. Furthermore, the fast ontology algorithm for standard ontology SVM by virtue of infinite push multi-dividing ontology algorithm is obtained. Finally, four experiments presented on various fields verify the efficiency of the new computation model for ontology similarity measuring and ontology mapping applications in multi-dividing setting. [ABSTRACT FROM AUTHOR]

The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As a semantic representation model, ontology has penetrated into all areas of natural science and social science. The core issue of ontology applications is similarity computing between ontology concepts. In this article, we report a sparse vector learning algorithm for ontology similarity measure and ontology mapping in terms of sub-gradient calculating and iterative computation. The main procedure of our iterative computation is based on the tricks of fuse and divide. The simulation experimental results show that the new proposed algorithm has high efficiency and accuracy in ontology similarity measure and ontology mapping in biology and physical education science. [ABSTRACT FROM AUTHOR]

Ontology is an effective tool for processing concept semantics, and in the ontology learning algorithm, all the semantic information of each vertex is expressed by a multidimensional vector. The essence of ontology learning algorithm is to obtain ontology function in terms of ontology data samples, so as to map each concept in ontology to a real number. Stability is the foundation of the ontology learning algorithm and the guarantee of its generalization ability. This article relaxes the original uniformly stable hypothesis and proposes the concept of locally ontology relaxed stability. And under the setting of reproducing kernel Hilbert space, the upper bound of stability is verified. Under the framework of random ontology algorithm, the original concept is redefined. The error bounds in general, the reproducing kernel Hilbert space and the stochastic ontology learning algorithm frameworks are obtained in terms of their respective stability definitions. [ABSTRACT FROM AUTHOR]

Ontology learning problem has raised much attention in semantic structure expression and information retrieval. As a powerful tool, ontology is evenly employed in various subjects, such as neuroscience, medical science, pharmacopedia, chemistry, education and other social science. Ontology similarity measuring plays a vital role in practical implementations since essential issues of ontology mapping are also similarity calculating. In ontology function learning, one learns a real valued score function that assigns scores to each ontology vertex which corresponds to a concept. Thus, the similarity between vertices is determined by means of the absolute value of difference between their corresponding scores. In this paper, we report the new optimization algorithms for obtaining ontology function in view of ontology sparse vector learning. The implementation of ontology algorithms is mainly based on iterative calculation in which we consider the whole matrix version of framework and ontology sparse vector are updated in each iterative. The data results obtained from four simulation experiments reveal that our newly proposed ontology approach has high efficiency and accuracy in biology and plant science with regard to ontology similarity measure, and humanoid robotics and education science with regard to ontology mapping. [ABSTRACT FROM AUTHOR]

Ontology, as an effective structured information storage, classification, and statistical tool, has been attached importance from researchers of various disciplines. At present, ontology has become the core study field of semantic network, artificial intelligence, and information retrieval. The core topic of ontology algorithm is to calculate the similarity between concepts, so as to obtain the potential information of each other. In this paper, we present the boosting based iterative learning algorithm to compute the ontology sparse vector, and thus get the ontology function which maps each ontology concept to a real number. Since the advantage of ontology sparse vector is dimensionality reduction, the algorithm can extract the key information from the high dimensional ontology representation data. At last, we select four classical ontologies to test the efficiency of new ontology algorithm, and the rest give the positive answer. [ABSTRACT FROM AUTHOR]