Analyzing l1-loss and l2-loss Support Vector Machines Implemented in PERMON Toolbox

  • Marek PechaEmail author
  • David Horák
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 554)


This paper deals with investigating l1-loss and l2-loss l2-regularized Support Vector Machines implemented in PermonSVM – a part of our PERMON toolbox. The loss functions quantify error between predicted and correct classifications of samples in cases of non-perfectly linearly separable classifications. In numerical experiments, we study properties of Hessians related to performance score of models and analyze convergence rate on 4 public available datasets. The Modified Proportioning and Reduced Gradient Projection algorithm is used as a solver for the dual Quadratic Programming problem resulting from Support Vector Machines formulations.


Support Vector Machines SVM PermonSVM Hinge loss functions Quadratic Programming QP MPRGP 



This work has been supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science - LQ1602; by Grant of SGS No. SP2018/165, VŠB - Technical University of Ostrava, Czech Republic and by the grant of the Czech Science Foundation (GACR) project no. GA17-22615S. The work has been also performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme; in particular, the author gratefully acknowledges the support of School of Mathematics, The University of Edinburgh, United Kingdom and the computer resources and technical support provided by Edinburgh Parallel Computing Centre (EPCC).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Applied MathematicsVŠB – Technical University of OstravaOstravaCzech Republic
  2. 2.Institute of Geonics CASOstravaCzech Republic

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