Statistical Modelling of Complex Emotions Using Mixture of Von Mises Distributions

The recognition of basic human emotions based on facial points has been studied extensively for many years. Since complex emotions are comprised of a number of the basic emotions, in order to identify them some way to interpolate between known basic emotions must be identified. In this paper, we introduce a finite mixture model to recognise complex emotions and represent them onto the activation-evaluation space, a popular model in psychology for emotion representation. Since the activation-evaluation space is circular, the popular probability distribution models for emotion recognition are inappropriate to characterise complex emotions. The model that we propose is based on a mixture of von Mises distributions, which is an approximation to the normal distribution when wrapped onto a circle and the most common model for describing directional data. This paper describes the process of estimating the parameters of the mixture model and tests the fit of an estimated model to a set of ground truth values of emotion direction and intensity.