Classification of Multiple Cancer Types in a Hyper Reproducing Kernel Hilbert Space

The classification of multiple cancer types based on the gene expression profiles is a challenging task. Support Vector Machines (SVM) have been applied to this aim but they rely on Euclidean distances that fail to reflect accurately the proximities among sample profiles. In this paper, we incorporate in the classical nu-SVM algorithm a linear combination of non-Euclidean dissimilarities. The weights of the combination are learnt in a HRKHS (Hyper Reproducing Kernel Hilbert Space) using an efficient Semidefinite Programming algorithm. This approach allow us to incorporate a smoothing term that penalizes the complexity of the family of distances and avoids overfitting. The experimental results suggest that the method proposed helps to reduce significantly the misclassification errors in several human cancer problems.