Marie Szafranski

Composite kernel learning

The Support Vector Machine is an acknowledged powerful tool for building classifiers, but it lacks flexibility, in the sense that the kernel is chosen prior to learning. Multiple Kernel Learning enables to learn the kernel, from an ensemble of basis kernels, whose combination is optimized in the learning process. Here, we propose Composite Kernel Learning to address the situation where distinct components give rise to a group structure among kernels. Our formulation of the learning problem encompasses several setups, putting more or less emphasis on the group structure. We characterize the convexity of the learning problem, and provide a general wrapper algorithm for computing solutions. Finally, we illustrate the behavior of our method on multi-channel data where groups correspond to channels.

KEOPS: Kernels organized into pyramids

Data representation is a crucial issue in signal processing and machine learning. In this work, we propose to guide the learning process with a prior knowledge describing how similarities between examples are organized. This knowledge is encoded in a tree structure that represents nested groups of similarities that are the pyramids of kernels. We propose a framework that learns a Support Vector Machine (SVM) on pyramids of arbitrary heights and identifies the relevant groups of similarities groups are relevant for classifying the examples. A weighted combination of (groups of) similarities is learned jointly with the SVM parameters, by optimizing a criterion that is shown to be an equivalent formulation regularized with a mixed norm of the original fitting problem. Our approach is illustrated on a Brain Computer Interfaces classification problem.