Unsupervised identification of nonstationary dynamical systems using a Gaussian mixture model based on EM clustering of SOMs

In this paper an effective unsupervised statistical identification technique for nonstationary nonlinear systems is presented. This technique extracts from the system outputs the multivariate relationships of the system natural modes, by means of the separation property of the Karhunen-Loève transform (KLT). Then, it applies a Self-Organizing Map (SOM) to the KLT output vectors in order to give an optimal representation of data. Finally, it exploits an optimized Expectation Maximization (EM) algorithm to find the optimal parameters of a Gaussian mixture model. The resulting statistical system identification is thus based on the estimation of the multivariate probability density function (PDF) of system outputs, whose convergence towards that computed by kernel estimation has also been proved by verifying the asymptotically vanishing of Kullback-Leibler divergences. A large number of simulations on ECG signals demonstrated the validity and the excellent performance of this technique along with its applicability to noninvasive diagnosis of a large class of medical pathologies originated by unknown, unpractical to measure, physiological factors.