Abstract. 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. 1

Generative embeddings use generative probabilistic models to project objects into a vectorial space of reduced dimensionality – where the so-called generative kernels can be defined. Some of these approaches employ generative models on latent variables to project objects into a feature space where the dimensions are related to the latent variables. Here, we propose to enhance the discriminative power of such spaces by performing a non-linear mapping of space dimensions leading to the formulation of novel generative kernels. In this paper, we investigate one possible non-linear mapping, based on a powering operation, able to equilibrate the contributions of each latent variable of the model, thus augmenting the entropy of the latent variables vectors. The validity of the idea has been shown in the case of two generative kernels, which have been evaluated with tests on shape recognition and gesture classification, with really satisfying results that outperform state-of-theart methods. 1.

Abstract. Many approaches to learning classifiers for structured objects (e.g., shapes) use generative models in a Bayesian framework. However, state-of-the-art classifiers for vectorial data (e.g., support vector machines) are learned discriminatively. A generative embedding is a mapping from the object space into a fixed dimensional feature space, induced by a generative model which is usually learned from data. The fixed dimensionality of these feature spaces permits the use of state of the art discriminative machines based on vectorial representations, thus bringing together the best of the discriminative and generative paradigms. Using a generative embedding involves two steps: (i) defining and learning the generative model used to build the embedding; (ii) discriminatively learning a (maybe kernel) classifier on the adopted feature space. The literature on generative embeddings is essentially focused on step (i), usually adopting some standard off-the-shelf tool (e.g., an SVM with a linear or RBF kernel) for step (ii). In this paper, we follow a different route, by combining several Hidden Markov Models-based generative embeddings (including the classical Fisher score) with the recently proposed non-extensive information theoretic kernels. We test this methodology on a 2D shape recognition task, showing that the proposed method is competitive with the state-of-art. 1

Abstract—Generative kernels have emerged in the last years as an effective method for mixing discriminative and generative approaches. In particular, in this paper, we focus on kernels defined on generative models with latent variables (e.g. the states in a Hidden Markov Model). The basic idea underlying these kernels is to compare objects, via a inner product, in a feature space where the dimensions are related to the latent variables of the model. Here we propose to enhance these kernels via a nonlinear normalization of the space, namely a nonlinear mapping of space dimensions able to exploit their discriminative characteristics. In this paper we investigate three possible nonlinear mappings, for two HMMbased generative kernels, testing them in different sequence classification problems, with really promising results. Keywords-nonlinear mappings; generative kernels; I.