Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China.
Graduate School of Information Science and Engineering, Ritsumeikan University, Shiga, Japan.
Neural Netw. 2019 Sep;117:179-190. doi: 10.1016/j.neunet.2019.05.009. Epub 2019 May 27.
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.
由于传感器干扰或极端动态，动力系统中通常存在噪声和异常值。因此，鲁棒性和泛化能力对于系统建模至关重要。本文提出了一种用于系统建模和大规模噪声混沌时间序列预测的鲁棒流形广义学习系统（RM-BLS）。流形嵌入用于发现混沌系统的演化。在特征选择过程中，通过特征选择丢弃与低维流形嵌入不相关的特征，从而随机破坏流形表示，这导致了一种鲁棒的学习范例，并实现了更好的泛化性能。我们还开发了一种用于斯蒂费尔流形优化的有效解决方案，其中通过 Cayley 变换和曲线搜索算法保持正交约束。此外，我们讨论了随机扰动逼近与其他主流正则化方法之间的共同思想。我们还证明了流形嵌入的扰动与 Tikhonov 正则化之间的等价性。大规模噪声混沌时间序列预测的仿真结果说明了我们方法的鲁棒性和泛化性能。
