Kernels for structured data are commonly obtained by decomposingobjects into their parts and adding up the similarities between all pairs of partsmeasured by a base kernel. Assignment kernels are based on an optimal bijectionbetween the parts and have proven to be an effective alternative to the establishedconvolution kernels. We explore how the base kernel can be learned as part ofthe classification problem. We build on the theory of valid assignment kernelsderived from hierarchies defined on the parts. We show that the weights of thishierarchy can be optimized via multiple kernel learning. We apply this result tolearn vertex similarities for the Weisfeiler-Lehman optimal assignment kernel forgraph classification. We present first experimental results which demonstrate thefeasibility and effectiveness of the approach.

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