Robust manifold broad learning system for large-scale noisy chaotic time series prediction: A perturbation perspective

Abstract

Noises and outliers commonly exist in dynamical systems because of sensor disturbations or extreme dynamics. Thus, the robustness and generalization capacity are of vital importance for system modeling. In this paper, the robust manifold broad learning system(RM-BLS) is proposed for system modeling and large-scale noisy chaotic time series prediction. Manifold embedding is utilized for chaotic system evolution discovery. The manifold representation is randomly corrupted by perturbations while the features not related to low-dimensional manifold embedding are discarded by feature selection. It leads to a robust learning paradigm and achieves better generalization performance. We also develop an efficient solution for Stiefel manifold optimization, in which the orthogonal constraints are maintained by Cayley transformation and curvilinear search algorithm. Furthermore, we discuss the common thoughts between random perturbation approximation and other mainstream regularization methods. We also prove the equivalence between perturbations to manifold embedding and Tikhonov regularization. Simulation results on large-scale noisy chaotic time series prediction illustrates the robustness and generalization performance of our method.