Abstract
This article proposes the multiclass proximal support vector machine (MPSVM) classifier, which extends the binary PSVM to the multiclass case. Unlike the one-versus-rest approach that constructs the decision rule based on multiple binary classification tasks, the proposed method considers all classes simultaneously and has better theoretical properties and empirical performance. We formulate the MPSVM as a regularization problem in the reproducing kernel Hilbert space and show that it implements the Bayes rule for classification. In addition, the MPSVM can handle equal and unequal misclassification costs in a unified framework. We suggest an efficient algorithm to implement the MPSVM by solving a system of linear equations. This algorithm requires much less computational effort than solving the standard SVM, which often requires quadratic programming and can be slow for large problems. We also provide an alternative and more robust algorithm for ill-posed problems. The effectiveness of the MPSVM is demonstrated by both simulation studies and applications to cancer classifications using microarray data.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 339-355 |
| Number of pages | 17 |
| Journal | Journal of Computational and Graphical Statistics |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2006 |
| Externally published | Yes |
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Keywords
- Bayes rule
- Nonstandard classifications
- Reproducing kernel Hilbert space
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Computational Mathematics
Cite this
Multiclass proximal support vector machines. / Tang, Yongqiang; Zhang, Hao.
In: Journal of Computational and Graphical Statistics, Vol. 15, No. 2, 06.2006, p. 339-355.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multiclass proximal support vector machines
AU - Tang, Yongqiang
AU - Zhang, Hao
PY - 2006/6
Y1 - 2006/6
N2 - This article proposes the multiclass proximal support vector machine (MPSVM) classifier, which extends the binary PSVM to the multiclass case. Unlike the one-versus-rest approach that constructs the decision rule based on multiple binary classification tasks, the proposed method considers all classes simultaneously and has better theoretical properties and empirical performance. We formulate the MPSVM as a regularization problem in the reproducing kernel Hilbert space and show that it implements the Bayes rule for classification. In addition, the MPSVM can handle equal and unequal misclassification costs in a unified framework. We suggest an efficient algorithm to implement the MPSVM by solving a system of linear equations. This algorithm requires much less computational effort than solving the standard SVM, which often requires quadratic programming and can be slow for large problems. We also provide an alternative and more robust algorithm for ill-posed problems. The effectiveness of the MPSVM is demonstrated by both simulation studies and applications to cancer classifications using microarray data.
AB - This article proposes the multiclass proximal support vector machine (MPSVM) classifier, which extends the binary PSVM to the multiclass case. Unlike the one-versus-rest approach that constructs the decision rule based on multiple binary classification tasks, the proposed method considers all classes simultaneously and has better theoretical properties and empirical performance. We formulate the MPSVM as a regularization problem in the reproducing kernel Hilbert space and show that it implements the Bayes rule for classification. In addition, the MPSVM can handle equal and unequal misclassification costs in a unified framework. We suggest an efficient algorithm to implement the MPSVM by solving a system of linear equations. This algorithm requires much less computational effort than solving the standard SVM, which often requires quadratic programming and can be slow for large problems. We also provide an alternative and more robust algorithm for ill-posed problems. The effectiveness of the MPSVM is demonstrated by both simulation studies and applications to cancer classifications using microarray data.
KW - Bayes rule
KW - Nonstandard classifications
KW - Reproducing kernel Hilbert space
UR - http://www.scopus.com/inward/record.url?scp=33745305029&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745305029&partnerID=8YFLogxK
U2 - 10.1198/106186006X113647
DO - 10.1198/106186006X113647
M3 - Article
AN - SCOPUS:33745305029
VL - 15
SP - 339
EP - 355
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
SN - 1061-8600
IS - 2
ER -