A novel framework for multi-class classification via ternary smooth support vector machine

Chih Cheng Chang, Li Jen Chien*, Yuh-Jye Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


This paper extends the previous work in smooth support vector machine (SSVM) from binary to k-class classification based on a single-machine approach and call it multi-class smooth SVM (MSSVM). This study implements MSSVM for a ternary classification problem and labels it as TSSVM. For the case k>3, this study proposes a one-vs.-one-vs.-rest (OOR) scheme that decomposes the problem into k(k-1)/2 ternary classification subproblems based on the assumption of ternary voting games. Thus, the k-class classification problem can be solved via a series of TSSVMs. The numerical experiments in this study compare the classification accuracy for TSSVM/OOR, one-vs.-one, one-vs.-rest schemes on nine UCI datasets. Results show that TSSVM/OOR outperforms the one-vs.-one and one-vs.-rest for all datasets. This study includes further error analyses to emphasize that the prediction confidence of OOR is significantly higher than the one-vs.-one scheme. Due to the nature of OOR design, it can detect the hidden (unknown) class directly. This study includes a "leave-one-class-out" experiment on the pendigits dataset to demonstrate the detection ability of the proposed OOR method for hidden classes. Results show that OOR performs significantly better than one-vs.-one and one-vs.-rest in the hidden-class detection rate.

Original languageEnglish
Pages (from-to)1235-1244
Number of pages10
JournalPattern Recognition
Issue number6
StatePublished - 1 Jun 2011


  • Confidence
  • Hidden classes
  • Multi-class classification
  • Smooth method
  • Support vector machine
  • Ternary voting games

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