Graph Echo State Network (GraphESN) is an efficient neural network model that extends the applicability of Reservoir Computing to the processing of graphs. The untrained reservoir encodes input graphs into isomorphic structured states. In this paper we propose a novel and supervised approach for adaptively weight the relevance of the states of the vertices in the input graphs for the output computation in classification tasks. To this aim, local average computations on partitions of the state space, obtained using the Neural Gas algorithm, are combined according to the target information. The effectiveness of the proposed approach is shown on real-world tasks from Cheminformatics.
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