Optimization of Kernel Alignment by Data Translation in Feature Space

Kernel-target alignment is commonly used to predict the behavior of reproducing kernels in a classification context, without training any kernel machine. In this paper, we show that a poor position of training data in feature space can drastically reduce the value of alignment. This implies that, in a kernel selection setting, the best kernel of a given collection may be characterized by a low alignment. To overcome this situation, we present a gradient ascent algorithm for maximizing the alignment by data translation in feature space. The aim is to reduce the biais introduced by the translation non-invariance of this criterion. Experimental results on multidimensional benchmarks show the effectiveness of our approach.