Doklady Mathematics

, Volume 93, Issue 2, pp 231–233 | Cite as

Mathematical knowledge ontologies and recommender systems for collections of documents in physics and mathematics

  • A. M. Elizarov
  • A. B. Zhizhchenko
  • N. G. Zhil’tsov
  • A. V. Kirillovich
  • E. K. Lipachev
Computer Science


An approach to the implementation of a recommender system based on ontologies of mathematical knowledge is presented. On the basis of a document browsed by a user, the system forms on line a list of recommendations, which include similar documents, key words, and definitions of these words from ontology and other terminological sources. The method of recommendations yields a vector representation of documents, taking into account the position of terms in the logical structure of the document and their ontological connections. On the basis of the cosine measure, a measure of proximity between documents is calculated. The order of documents in the list of recommendations is determined by values of the proximity measure. Various adaptations of the system to user scenarios aimed at the preparation of personalized recommendations are discussed.


DOKLADY Mathematic Logical Structure Ontology Term User Scenario Proximity Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Recommender Systems Handbook, Ed. by F. Ricci, L. Rokach, B. Shapira, and P. B. Kantor (Springer, New York, 2011).zbMATHGoogle Scholar
  2. 2.
    J. Bobadilla, F. Ortega, A. Hernando, and A. Gutierrez, Knowledge-Based Systems 46, 109–132 (2013).CrossRefGoogle Scholar
  3. 3.
    A. S. Lampropoulos and G. A. Tsihrintzis, Machine Learning Paradigms: Applications in Recommender Systems (Springer Intern. Publ., Cham, 2015).CrossRefGoogle Scholar
  4. 4.
    K. Verbert, N. Manouselis, X. Ochoa, M. Wolpers, H. Drachsler, I. Bosnic, and E. Duval, IEEE Trans. Learning Technol. 5 (4), 318–335 (2012).CrossRefGoogle Scholar
  5. 5.
    S. E. Middleton, D. De Roure, and N. R. Shadbolt, in Handbook on Ontologies (Springer-Verlag, Berlin, 2009), pp. 779–796.CrossRefGoogle Scholar
  6. 6.
    A. M. Elizarov, E. K. Lipachev, O. A. Nevzorova, and V. D. Solov’ev, Dokl. Math. 90 (1), 521–524 (2014).MathSciNetCrossRefGoogle Scholar
  7. 7.
    A. M. Elizarov, A. V. Kirillovich, E. K. Lipachev, O. A. Nevzorova, V. D. Solovyev, and N. G. Zhiltsov, Lobachevskii J. Math. 35 (4), 347–353 (2014).MathSciNetCrossRefGoogle Scholar
  8. 8.
    O. Nevzorova, N. Zhiltsov, A. Kirillovich, and E. Lipachev, in Knowledge Engineering and the Semantic Web (Springer Intern. Publ., Berlin, 2014), pp. 105–119.zbMATHGoogle Scholar
  9. 9.
    V. Solovyev and N. Zhiltsov, Proceedings of International Conference on Web Intelligence, Mining and Semantics (ACM, London, 2011).Google Scholar
  10. 10.
    K. Aberer, A. Boyarsky, P. Cudré-Mauroux, G. Demartini, and O. Ruchayskiy, Tenth International Semantic Web Conference ISWC 2011-Demo (Bonn, 2011).Google Scholar
  11. 11.
    A. B. Zhizhchenko and A. D. Izaak, Russ. Math. Surveys 62 (5), 943–966 (2007).MathSciNetCrossRefGoogle Scholar
  12. 12.
    D. Chebukov, A. Izaak, O. Misurina, Yu. Pupyrev, and A. Zhizhchenko, Lect. Notes Comput. Sci. 7961, 344–348 (2013).CrossRefGoogle Scholar
  13. 13.
    W. Shen, J. Wang, and J. Han, IEEE Trans. Knowledge Data Eng. 27 (2), 443–460 (2015).CrossRefGoogle Scholar
  14. 14.
    O. Nevzorova, N. Zhiltsov, D. Zaikin, O. Zhibrik, A. Kirillovich, V. Nevzorov, and E. Birialtsev, in The Semantic Web–ISWC (Springer-Verlag, Berlin, 2013), pp. 379–394.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • A. M. Elizarov
    • 1
  • A. B. Zhizhchenko
    • 2
  • N. G. Zhil’tsov
    • 3
  • A. V. Kirillovich
    • 3
  • E. K. Lipachev
    • 1
  1. 1.Institute of Mathematics and MechanicsKazan Federal UniversityKazanRussia
  2. 2.Joint Supercomputer CenterRussian Academy of SciencesMoscowRussia
  3. 3.Higher Institute of Information Technologies and Information SystemsKazan Federal UniversityKazanRussia

Personalised recommendations