The modified sufficient conditions for echo state property and parameter optimization of leaky integrator echo state network
| Autor: | Xian-shuang Yao, Hai-feng Hu, Shu-xian Lun |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Quantitative Biology::Neurons and Cognition Artificial neural network Spectral radius Computer science Echo (computing) Feed forward Leaky integrator 02 engineering and technology Dynamical system Matrix (mathematics) 020901 industrial engineering & automation Control theory 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Echo state network Software Eigenvalues and eigenvectors |
| Zdroj: | Applied Soft Computing. 77:750-760 |
| ISSN: | 1568-4946 |
| DOI: | 10.1016/j.asoc.2019.02.005 |
| Popis: | Leaky integrator echo state network (Leaky-ESN), an improved echo state network, is suitable for learning very slow dynamic systems and replaying the learnt system at different speeds. To ensure the echo state property of Leaky-ESN, spectral radius of reservoir connection weight matrix needs to be less than leaking rate, which means that the output feedback of Leaky-ESN is actually ignored. Leaky-ESN without output feedback is equivalent to being a feedforward type neural network. Therefore, in this paper, we consider Leaky-ESN model with output feedback. Firstly, we give the modified sufficient conditions for echo state property, which are actually some inequality constraints about the control parameters (mainly leaking rate, spectral radius of reservoir connection weight matrix and the scaling of output feedback) and the maximum singular values of feedback and output connection weight matrices. Secondly, to reduce the influence of the initial values of the control parameters on Leaky-ESN, we use the barrier method to optimize the control parameters. The barrier method can convert the constrained optimization problem into the unconstrained optimization problem. Newton’s method and its improve method, for example, eigenvalue modification methods, are further used to solve the unconstrained optimization problem and then obtain the control parameters of Leaky-ESN. Finally, Mackey–Glass chaotic time series prediction is selected to validate the method proposed in this paper. Simulation results show that the method proposed in this paper can make Leaky-ESN model more stable and higher approximation precision. |
| Databáze: | OpenAIRE |
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