Pyramides de noyaux
Statistical learning aims at predicting, but also at analyzing and interpreting a phenomenon. In this process, data representation is a crucial issue. We propose to guide the learning process by providing it with a prior knowledge describing how similarities between examples are organized. This knowledge is encoded as a “kernel pyramid”, that is, a tree structure that represents nested groups and sub-groups of similarities. Provided few (groups of) similarities are relevant for the classifying the observations, our approach identifies these similarities. We propose herein the first complete solution to this problem, enabling to learn a Support Vector Machine (SVM) on pyramids of arbitrary heights. A weighted combination of (groups of) similarities is learned jointly with the SVM parameters, by optimizing a criterion that is shown to be a variational formulation of the original fitting problem penalized by a mixed norm. We illustrate our approach on the recognition of facial expressions from still images, whose features are described by a pyramid depicting the spatial and scale parameters of the wavelet decomposition of the original image.