Complexity reduction and parameter selection in support vector machines

We focus on two central issues regarding the application of support vector machines (SVM) for classification in real contexts. The first one deals with the reduction of the computational complexity of a reference classifier during the test phase, without increasing the generalization error of the classifier. In particular, we show that the complexity in the test phase can be reduced by training SVM classifiers on a new set of uncorrelated features obtained by using the principal component analysis and explicitly mapping the new input space in the feature space induced by the adopted kernel function. The second issue deals with the problem of parameter selection. In particular we show that the receiver operating characteristic curves, measured on a suitable validation set, are effective for selecting among the classifiers the machine implements the one having performances similar to the reference classifier. We address these two issues in the context of object detection in images and in particular for the specific problem of detecting goal during a football match