http://www.stat.ohio-state.edu/~yklee/msvm.htm

Two-category support vector machines (SVM) have been very popular in the machine learning community for classi cation problems. Solving multicategory problems by a series of binary classi ers 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 misclassi cation 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 classi cation using microarray data and cloud classi cation with satellite radiance pro les.

No abstract

Normalization of expression levels applied to microarray data can help in reducing measurement error. Different methods, including cyclic loess, quantile normalization and median or mean normalization, have been utilized to normalize microarray data. Although there is considerable literature regarding normalization techniques for mRNA microarray data, there are no publications comparing normalization techniques for microRNA (miRNA) microarray data, which are subject to similar sources of measurement error. In this paper, we compare the performance of cyclic loess, quantile normalization, median normalization and no normalization for a single-color microRNA microarray dataset. We show that the quantile normalization method works best in reducing differences in miRNA expression values for replicate tissue samples. By showing that the total mean squared error are lowest across almost all 36 investigated tissue samples, we are assured that the bias correction provided by quantile normalization is not outweighed by additional error variance that can arise from a more complex normalization method. Furthermore, we show that quantile normalization does not achieve these results by compression of scale.