期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 49, 期 6, 页码 2305-2315出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2018.2825253
关键词
Chaotic time series; L-1/2-norm penalty; L-2-norm penalty; prediction; regularization
类别
资金
- National Natural Science Foundation of China [61702077, 61773087, 61672131, 61374154]
- Fundamental Research Funds for the Central Universities [DUT16RC(3) 123, DUT17ZD216]
Multivariate chaotic time series prediction is a hot research topic, the goal of which is to predict the future of the time series based on past observations. Echo state networks (ESNs) have recently been widely used in time series prediction, but there may be an ill-posed problem for a large number of unknown output weights. To solve this problem, we propose a hybrid regularized ESN, which employs a sparse regression with the L(1/2 )regularization and the L-2 regularization to compute the output weights. The L-1/2 penalty shows many attractive properties, such as unbiasedness and sparsity. The L-2 penalty presents appealing ability on shrinking the amplitude of the output weights. After the output weights are calculated, the input weights, internal weights, and output weights are fine-tuning by a Hessian-free optimization method-conjugate gradient back-propagation algorithm. The fine-tuning helps to bubble up the input information toward the output layer. Besides, the largest Lyapunov exponent is used to calculate the predictable horizon of a chaotic time series. Experimental results on benchmark and real-world datasets show that our proposed method is superior to other ESN-based models, as sparser, smaller-absolute-value, and more informative output weights are obtained. All of the predictions within the predictable horizon of the proposed model are accurate.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据