κ-NN for the classification of human cancer samples using the gene expression profiles

The [Formula: see text]-Nearest Neighbor (k-NN) classifier has been applied to the identification of cancer samples using the gene expression profiles with encouraging results. However, the performance of [Formula: see text]-NN depends strongly on the distance considered to evaluate the sample proximities. Besides, the choice of a good dissimilarity is a difficult task and depends on the problem at hand. In this chapter, we introduce a method to learn the metric from the data to improve the [Formula: see text]-NN classifier. To this aim, we consider a regularized version of the kernel alignment algorithm that incorporates a term that penalizes the complexity of the family of distances avoiding overfitting. The error function is optimized using a semidefinite programming approach (SDP). The method proposed has been applied to the challenging problem of cancer identification using the gene expression profiles. Kernel alignment [Formula: see text]-NN outperforms other metric learning strategies and improves the classical [Formula: see text]-NN algorithm.