Dynamical pattern recognition for sampling sequences based on deterministic learning and structural stability

Abstract

This paper focuses on the recognition problem of dynamical patterns consisting of sampling sequences. Specifically, based on the concept of structural stability, a novel similarity measure for dynamical patterns is first given. Then, a specific realization is provided, which consists of: (1) an approximation scheme for computation of partial derivative information by utilizing the knowledge learned through deterministic learning; (2) a similarity comparison scheme using the recognition errors generated from the discrete-time dynamical estimators; and (3) performance analysis of the recognition scheme with general recognition conditions. Compared with the existing methods, in which misrecognition may occur when the differences of dynamics between adjacent training patterns are very small, the proposed method is more appealing in the sense that, the partial derivatives of dynamics are introduced to complement the similarity measures, such that the recognition performance is much improved. Simulation studies are conducted to verify the proposed method in a relatively large data set.