Generative kernels represent theoretically grounded tools able to increase the capabilities of generative classification through a discriminative setting. Fisher Kernel is the first and mostly-used representative, which lies on a widely investigated mathematical background. The manufacture of a generative kernel flows down through a two-step serial pipeline. In the first, “generative” step, a generative model is trained, considering one model for class or a whole model for all the data; then, features or scores are extracted, which encode the contribution of each data point in the generative process. In the second, “discriminative” part, the scores are evaluated by a discriminative machine via a kernel, exploiting the data separability. In this paper we contribute to the first aspect, proposing a novel way to fit the class-data with the generative models, in specific, focusing on Hidden Markov Models (HMM). The idea is to perform model clustering on the unlabeled data in...