Clustering-Based Construction of Hidden Markov Models for Generative Kernels

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 order to discover at best the structure of the entire sample set. Then, the label information is retrieved and generative scores are computed. Experimental, comparative test provides a preliminary idea on the goodness of the novel approach, pushing forward for further developments.