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

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Book cover AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application (AETA 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 554))

Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Applied Mathematics, VŠB – Technical University of Ostrava, Ostrava, Czech Republic

    Marek Pecha & David Horák

  2. Institute of Geonics CAS, Ostrava, Czech Republic

    Marek Pecha & David Horák

Authors
  1. Marek Pecha
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  2. David Horák
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Corresponding author

Correspondence to Marek Pecha .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Electrical Engineering, VŠB-TUO, Ostrava-Poruba, Czech Republic

    Ivan Zelinka

  2. Department of Electronics, Faculty of Electrical Engineering, VŠB-TUO, Ostrava, Czech Republic

    Pavel Brandstetter

  3. International Cooperation, Research and Training Institute, Ton Duc Thang University, Ho Chi Minh, Vietnam

    Tran Trong Dao

  4. Department of Automatic Control, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vo Hoang Duy

  5. Department of Mechanical Design Engineering, Pukyong National University, Busan, Korea (Republic of)

    Sang Bong Kim

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Pecha, M., Horák, D. (2020). Analyzing l1-loss and l2-loss Support Vector Machines Implemented in PERMON Toolbox. In: Zelinka, I., Brandstetter, P., Trong Dao, T., Hoang Duy, V., Kim, S. (eds) AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2018. Lecture Notes in Electrical Engineering, vol 554. Springer, Cham. https://doi.org/10.1007/978-3-030-14907-9_2

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  • DOI: https://doi.org/10.1007/978-3-030-14907-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14906-2

  • Online ISBN: 978-3-030-14907-9

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