The human-machine interface (HMI) using gesture recognition system as core technologies have been popularized in the videogame industry in the last half decade. In this paper we propose a mathematical model to analyze human gestures through the implementation of Kinect sensor, for the interpretation of gestures and body movements. We use a mathematical technique called Gaussian Process Dynamical Models (GPDM) in addition to motion capture data processed with an interface developed, our goal is to train an algorithm that allows the classification of gestures and perform a statistical analysis of the data in a simulation environment, which uses techniques of digital animation and communication interface for interactive gestures. We found that for each gesture to classify exists a set of hyper-parameters characterizing the model, which are described by two cores: one linear and a radial basis function (RBF). Finally the mathematical data classification is performed by calculating the logarithm of the posterior of the GPDM model for each new data set. This type of model can have a high impact on processes of computer assisted rehabilitation.