Smoothed Generalized Dirichlet: A Novel Count-Data Model for Detecting Emotional States

Abstract

In this article, we propose novel approaches to deal with the problem of burstiness, the challenge of count-data sparseness, and the curse of dimensionality. We introduce a smoothed generalized Dirichlet distribution that is a smoothed variant of the generalized Dirichlet distribution and a generalization of the smoothed Dirichlet. We provide different learning methods based on mixture models and agglomerative clustering-based geometrical information: Kullback–Leibler divergence, Fisher metric, and Bhattacharyya distance. Moreover, we show that the new smoothed generalized Dirichlet could be considered as a prior to the multinomial, which generates a new distribution for count data that we call the smoothed generalized Dirichlet multinomial. In particular, we present an approximation based on Taylor series expansion for better performance and optimized running time in the case of high-dimensional count data. The proposed models are evaluated through two emotion detection applications: disaster-tweet-related emotions and pain intensity estimation. Experiments show the efficiency and the robustness of our approaches when dealing with texts, videos, and images.