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Multicategory support vector machines: theory and application to the classification of microarray data and satellite radiance data. (English) Zbl 1089.62511
Summary: Two-category support vector machines (SVM) have been very popular in the machine learning community for classification problems. Solving multicategory problems by a series of binary classifiers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which extends the binary SVM to the multicategory case and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassification costs. As a tuning criterion for the MSVM, an approximate leave-one-out cross-validation function, called Generalized Approximate Cross Validation, is derived, analogous to the binary case. The effectiveness of the MSVM is demonstrated through the applications to cancer classification using microarray data and cloud classification with satellite radiance profiles.

62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T05 Learning and adaptive systems in artificial intelligence
62P10 Applications of statistics to biology and medical sciences; meta analysis
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