Logistic support vector machines and their application to gene expression data

One important feature of the gene expression data is that the number of genes m far exceeds the number of samples n. When applied to analyse the gene expression data, standard statistical methods do not work well when n < m. Development of new methodologies or modification of existing methodologies is needed for the analysis of microarray data. Support vector machine (SVM) has been applied in gene expression data classification. In traditional SVM classification, a classifier is usually built by a small subset of samples called support vectors. This may cause a loss of available information since the number of samples in a gene expression dataset is usually very small. In this paper, we introduce a logistic support vector machine (LSVM) algorithm for the classification task. In LSVM, all the samples are used as support vectors and parameters are estimated via the maximum a posteriori (MAP) estimation procedure. The proposed algorithm also has the advantage of providing an estimate of the underlying probability. This algorithm was applied to five different gene expression datasets. Computational results show that compared with popular classification methods such as traditional SVM, our algorithm usually leads to an improvement in classification accuracy.