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Gene selection and prediction for cancer classification using support vector machines with a reject option. (English) Zbl 1328.62586
Summary: In cancer classification based on gene expression data, it would be desirable to defer a decision for observations that are difficult to classify. For instance, an observation for which the conditional probability of being cancer is around 1/2 would preferably require more advanced tests rather than an immediate decision. This motivates the use of a classifier with a reject option that reports a warning in cases of observations that are difficult to classify. In this paper, we consider a problem of gene selection with a reject option. Typically, gene expression data comprise of expression levels of several thousands of candidate genes. In such cases, an effective gene selection procedure is necessary to provide a better understanding of the underlying biological system that generates data and to improve prediction performance. We propose a machine learning approach in which we apply the $$l_{1}$$ penalty to the SVM with a reject option. This method is referred to as the $$l_{1}$$ SVM with a reject option. We develop a novel optimization algorithm for this SVM, which is sufficiently fast and stable to analyze gene expression data. The proposed algorithm realizes an entire solution path with respect to the regularization parameter. Results of numerical studies show that, in comparison with the standard $$l_{1}$$ SVM, the proposed method efficiently reduces prediction errors without hampering gene selectivity.

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62J07 Ridge regression; shrinkage estimators (Lasso) 62-07 Data analysis (statistics) (MSC2010)
##### Keywords:
classification; reject option; support vector machines; lasso
##### Software:
SparseLOGREG; LASSO
Full Text:
##### References:
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