A multi-class SVM approach based on the l1-norm minimization of the distances between the reduced convex hulls.

Miguel Carrasco, Julio López, Sebastián Maldonado*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Multi-class classification is an important pattern recognition task that can be addressed accurately and efficiently by Support Vector Machine (SVM). In this work we present a novel SVM-based multi-class classification approach based on the center of the configuration, a point which is equidistant to all classes. The center of the configuration is obtained from the dual formulation by minimizing the distances between the reduced convex hulls using the l1-norm, while the decision functions are subsequently constructed from this point. This work also extends the ideas of Zhou et al. (2002) [37] to multi-class classification. The use of l1-norm provides a single linear programming formulation, which reduces the complexity and confers scalability compared with other multi-class SVM methods based on quadratic programming formulations. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance and running times compared with various other multi-class SVM methods.

Original languageEnglish
Pages (from-to)1598-1607
Number of pages10
JournalPattern Recognition
Issue number5
StatePublished - 1 May 2015

Bibliographical note

Funding Information:
The authors are grateful to the anonymous reviewers who contributed to improving the quality of the original paper. The first author was supported by FONDECYT Project 1130905 , the second by FONDECYT Project 11110188 and CONICYT Anillo ACT1106 , and the third by FONDECYT Project 11121196 .

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.


  • Linear programming
  • Multi-class classification
  • Support vector machines


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