In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.
Due to the lack of space, we do not cover related works on semantic data analysis for mathematical texts, which are given in @cite_13 @cite_2 .
@cite_13 @cite_2
2015651633 2041540188 1974087593 2120779048
A survey of the key approaches to the semantic processing of mathematical texts is presented. A software platform prototype for the electronic storage of mathematical documents, which is based on the linked open-data (LOD) model and uses semantic information for data management, including formula-fragment searching, is proposed. The analysis of mathematical documents and the extraction of semantic information from the latter are carried out based on the electronic collection of the Izv. Vyssh. Uchebn. Zaved., Mat. (1995---2009) using special-purpose ontologies, metadata representation in the RDF (Resource Description Framework) format, and integration with existing LOD sets. This paper analyzes two models: semantic annotation of mathematical texts and semantic searching for mathematical texts in a marked-up collection. It also presents the results of a series of experiments that were performed with a semantically annotated collection of scientific publications in the field of mathematics. This paper presents the analysis and modelling of two data sets associated with the literature of hypertext as represented by the ACM Hypertext conference series. This work explores new ways of organising and accessing the vast amount of interrelated information. The first data set, including all the full papers published in this series (1987 1998), is structured and visualised as a semantic space. This semantic space provides an access point for each paper in this collection. The second data set, containing author co-citation counts based on nine conferences in the series (1989 1998), is analysed and mapped in its entirety and in three evenly distributed sub-periods. Specialties  major research fronts in the field of hypertext  are identified based on the results of a factor analysis and corresponding author co-citation maps. The names of authors in these maps are linked to the bibliographical and citation summaries of these authors on the WWW. Computing semantic relatedness of natural language texts requires access to vast amounts of common-sense and domain-specific world knowledge. We propose Explicit Semantic Analysis (ESA), a novel method that represents the meaning of texts in a high-dimensional space of concepts derived from Wikipedia. We use machine learning techniques to explicitly represent the meaning of any text as a weighted vector of Wikipedia-based concepts. Assessing the relatedness of texts in this space amounts to comparing the corresponding vectors using conventional metrics (e.g., cosine). Compared with the previous state of the art, using ESA results in substantial improvements in correlation of computed relatedness scores with human judgments: from r = 0.56 to 0.75 for individual words and from r = 0.60 to 0.72 for texts. Importantly, due to the use of natural concepts, the ESA model is easy to explain to human users.