Combining Dissimilarities in a Hyper Reproducing Kernel Hilbert Space for Complex Human Cancer Prediction

Support Vector Machines (SVM) have been applied to the classification of cancer samples using the gene expression profiles. However, they rely on Euclidean distances that fail to reflect accurately the proximities among sample profiles. Then, non Euclidean dissimilarities provide additional information that should be considered to reduce the misclassification errors. 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 the misclassification errors in several human cancer problems.