Riemannian dynamic generalized space quantization learning

Abstract

Many existing works represent signals by covariance matrices and then develop learning methods on the Riemannian symmetric positive-definite (SPD) manifold to deal with such data. However, they summarize each instance with a single covariance matrix, omitting some potential important information, such as the time evolution of the correlation in signals. In this paper, we represent each instance by a sequence of covariance matrices and develop a novel dynamic generalized learning Riemannian space quantization (DGLRSQ) method to deal with such data representations. The proposed DGLRSQ method incorporates short-term memory mechanism in generalized learning Riemannian space quantization (GLRSQ), which is an extension of Euclidean generalized learning vector quantization to deal with SPD matrix-valued data. The proposed method can capture the temporal evolution of the correlation in signals and thus provides better performance to its the counterpart – GLRSQ, which treats each instance as a signal covariance matrix. Empirical investigations on synthetic data and motor imagery EEG data show the superior performance of the proposed method.