Multiresolution Kernels

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures and takes advantage of a more detailed "bag of components" representation of the objects. To obtain such a detailed description, we consider possible decompositions of the original bag into a collection of nested bags, following a prior knowledge on the objects' structure. We then consider these smaller bags to compare two objects both in a detailed perspective, stressing local matches between the smaller bags, and in a global or coarse perspective, by considering the entire bag. This multiresolution approach is likely to be best suited for tasks where the coarse approach is not precise enough, and where a more subtle mixture of both local and global similarities is necessary to compare objects. The approach presented here would not be computationally tractable without a factorization trick that we introduce before presenting promising results on an image retrieval task.