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This paper presents a family of methods for the design of adaptive kernels for tree-structured data that exploits the summarization properties of hidden states of hidden Markov models for trees. We introduce a compact and discriminative feature space based on the concept of hidden states multisets and we discuss different approaches to estimate such hidden state encoding. We show how it can be used to build an efficient and general tree kernel based on Jaccard similarity. Furthermore, we derive an unsupervised convolutional generative kernel using a topology induced on the Markov states by a tree topographic mapping. This paper provides an extensive empirical assessment on a variety of structured data learning tasks, comparing the predictive accuracy and computational efficiency of state-of-the-art generative, adaptive, and syntactical tree kernels. The results show that the proposed generative approach has a good tradeoff between computational complexity and predictive performance, in particular when considering the soft matching introduced by the topographic mapping. [ABSTRACT FROM AUTHOR]