Abstract: We propose in this article a new 3D shape classification and retrieval method, based on a supervised selection of the most significant features in a space of attributed extended Reeb graphs encoding different shape characteristics. The similarity between pairs of graphs is addressed through both their representation as set of bags of shortest paths, and the definition of kernels adapted to these descriptions. A multiple kernel learning algorithm is used on this set of kernels to find an optimal linear combination of kernels for classification and retrieval purposes. Results on classical data sets are comparable with the best results of the literature, and the modularity and flexibility of the kernel learning ensure its applicability to a large set of methods.