Investigating Convergence of Linear SVM Implemented in PermonSVM Employing MPRGP Algorithm

  • Jakub KružíkEmail author
  • Marek Pecha
  • Václav Hapla
  • David Horák
  • Martin Čermák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11087)


This paper deals with the novel PermonSVM machine learning tool. PermonSVM is a part of our PERMON toolbox. It implements the linear two-class Support Vector Machines. PermonSVM is built on top of PermonQP (PERMON module for quadratic programming) which in turn uses PETSc. The main advantage of PermonSVM is that it is parallel. The parallelism comes from a distribution of matrices and vectors. The MPRGP algorithm, implemented in PermonQP, is used as a solver of the quadratic programming problem arising from the dual SVM formulation. The scalability of MPRGP was proven in problems of mechanics with more than billion of unknowns solved on tens of thousands of cores. Apart from the scalability of our approach, we also investigate the relations between training rate, hyperplane margin, the value of the dual functional, and the norm of the projected gradient.


Support Vector Machines SVM PERMON PermonSVM PermonQP MPRGP Quadratic programming QP 



This work was supported by the Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science (LQ1602), and from the Large Infrastructures for Research, Experimental Development and Innovations project IT4Innovations National Supercomputing Center (LM2015070); by the internal student grant competition project SGS No. SP2018/165; by projects LO1404: Sustainable development of CENET, and CZ.1.05/2.1.00/19.0389: Research Infrastructure Development of the CENET; and by the Czech Science Foundation (GACR) projects no. 15-18274S and 17-22615S. We would also like to acknowledge partners in the ExCAPE project for providing us with training datasets related to the Pfam protein database.


  1. 1.
    ExCAPE: exascale compound activity prediction.
  2. 2.
    LIBSVM data: classification, regression, and multi-label.
  3. 3.
    IT4Innovations: Salomon cluster documentation - hardware overview. National Supercomputing Center, VSB-Technical University of Ostrava (2017).
  4. 4.
    Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Rupp, K., Smith, B.F., Zhang, H.: PETSc - Portable, Extensible Toolkit for Scientific Computation.
  5. 5.
    Brown, M., Grundy, W., Lin, D., Cristianini, N., Sugnet, C., Furey, T., Ares Jr., M., Haussler, D.: Knowledge-based analysis of microarray gene expression data by using support vector machines. Proc. Nat. Acad. Sci. U.S.A. 97(1), 262–267 (2000)CrossRefGoogle Scholar
  6. 6.
    Cherkassky, V., Mulier, F.M.: Learning from Data: Concepts, Theory, and Methods. Wiley-IEEE Press, Hoboken (2007)CrossRefGoogle Scholar
  7. 7.
    Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)zbMATHGoogle Scholar
  8. 8.
    Dostál, Z.: Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities. SOIA, vol. 23. Springer, New York (2009). Scholar
  9. 9.
    Foody, G.M., Mathur, A.: The use of small training sets containing mixed pixels for accurate hard image classification: training on mixed spectral responses for classification by a SVM. Remote Sens. Environ. 103(2), 179–189 (2006)CrossRefGoogle Scholar
  10. 10.
    Hapla, V., Horák, D., Pecha, M.: PermonSVM (2017).
  11. 11.
    Hapla, V., Horák, D., Čermák, M., Kružík, J., Pospíšil, L., Sojka, R.: PermonQP (2015).
  12. 12.
    Horak, D., Dostal, Z., Hapla, V., Kruzik, J., Sojka, R., Cermak, M.: Projector-less TFETI for contact problems: preliminary results. In: Civil-Comp Proceedings, vol. 111 (2017)Google Scholar
  13. 13.
    Ma, J., Saul, L., Savage, S., Voelker, G.: Identifying suspicious URLs: an application of large-scale online learning, pp. 681–688 (2009). Cited By 173Google Scholar
  14. 14.
    Munson, T., Sarich, J., Wild, S., Benson, S., McInnes, L.C.: TAO users manual. Technical report ANL/MCS-TM-322. Argonne National Laboratory (2015).
  15. 15.
    Rychetsky, M.: Algorithms and Architectures for Machine Learning Based on Regularized Neural Networks and Support Vector Approaches (Berichte Aus Der Informatik). Shaker Verlag GmbH, Herzogenrath (2001)Google Scholar
  16. 16.
    Shi, J., Lee, W.J., Liu, Y., Yang, Y., Wang, P.: Forecasting power output of photovoltaic systems based on weather classification and support vector machines. IEEE Trans. Ind. Appl. 48(3), 1064–1069 (2012)CrossRefGoogle Scholar
  17. 17.
    Smith, B.F., et al.: PETSc users manual. Technical report ANL-95/11 - Revision 3.5. Argonne National Laboratory (2016).
  18. 18.
    Vishnu, A., Narasimhan, J., Holder, L., Kerbyson, D., Hoisie, A.: Fast and accurate support vector machines on large scale systems. In: 2015 IEEE International Conference on Cluster Computing, pp. 110–119, September 2015Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jakub Kružík
    • 1
    • 2
    Email author
  • Marek Pecha
    • 1
    • 2
    • 3
  • Václav Hapla
    • 3
    • 4
  • David Horák
    • 1
    • 2
    • 3
  • Martin Čermák
    • 1
    • 2
    • 3
    • 5
  1. 1.IT4Innovations National Supercomputing CenterVŠB - Technical University of OstravaOstravaCzech Republic
  2. 2.Institute of Geonics CASOstravaCzech Republic
  3. 3.Department of Applied MathematicsVŠB - Technical University of OstravaOstravaCzech Republic
  4. 4.Department of Earth SciencesETH ZurichZürichSwitzerland
  5. 5.ENET CentreVŠB - Technical University of OstravaOstravaCzech Republic

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