Radial basis function kernel optimization for Support Vector Machine classifiers

Since the inception of SVMs [1], the interest for this kind of supervised learning method has only grown over the years [2], so that it has become a well established tool both for classification and regression [3]. SVMs are regarded as the most prominent exemplar of kernel methods, which solve complex machine learning problems by using linear estimation methods on a high dimensional feature space [4]. They are intensely employed in a myriad of applications, including object segmentation [5], video surveillance [6], drug discovery [7], and cancer genomics [8]. The SVM framework models a classification problem as a maximum margin optimization problem, where the decision boundary that has the largest distance (margin) to separate the training points of different classes is searched. There is a primal form of the optimization problem, where the weights to be optimized are associated with the input features, i.e., there is one weight per each input feature. There is also a dual form, where the weights are associated with the training samples, i.e., one weight per each training sample. In the dual form, the weights are Lagrange multipliers of a suitable Lagrangian function. The fewer variables to be optimized, the easier the optimization problem, so dual formulations are preferred for classification tasks with many input features [9]. This work has been submitted to the IEEE for possible publication.