Improvement of the Gaussian mixture models' unsupervised learning method through the inclusion of dynamical systems for various types of nonlinear data.

Gaussian mixture models (GMM) with a modulating dynamical system (DS) approach is an unsupervised learning method, and it can estimate the distribution of given data or encoding trajectories in the input space. In this paper, a series of trajectories is considered for simulation, and the role of tuning parameters in the algorithm for both Gaussian function encoding and behavior of the dynamical system is obtained and compared. This algorithm divides the input space of the data into presupposed local regions and then in each local region of the data employs a dynamical system approach for tracking the major trajectories of the data. In this paper, the influence of the number of the Gaussian function in the GMM approach is investigated and simulated deeply. Furthermore, the influence of the local statistical characteristic of data such as mean or covariance of the data on the training process is discussed, and in these conditions, the effect of tuning parameters as the number of the Gaussian function is explained. Also, all details of the characteristic of DS depend on these tuning parameters, especially when data has more variance or noise, this adjustment should be checked more accurately. So, eventually, we showed in the obtained simulation results that the behavior and location of attractor points in DS on the data distributions and accordingly stability of the DS is getting improved drastically by tuning the number of Gaussian functions accurately.