Dynamical system classification with diffusion embedding for ECG-based person identification

The problem of system classification consists of identifying the source system corresponding to a certain output signal. In the context of dynamical systems, the outputs are usually given in the form of time series, and this identification process includes determining the underlying states of the system or their intrinsic set of parameters. In this work we propose a general framework for classification and identification based on a manifold learning algorithm. This data-driven approach provides a low-dimensional representation of the system's intrinsic variables, which enables the natural organization of points in time as a function of their dynamics. By leveraging the diffusion maps algorithm, a particular manifold learning method, we are not only able to distinguish between different states of the same system but also to discriminate different systems altogether. We construct a classification scheme based on a notion of distance between the distributions of embedded samples for different classes, and propose three ways of measuring such separation. The proposed method is demonstrated on a synthetic example and later applied to the problem of person identification from ECG recordings. Our approach obtains a 97.25% recognition accuracy over a database of 90 subjects, the highest accuracy reported for this database.