Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Chaos. 2012 Sep;22(3):033127. doi: 10.1063/1.4746765.
Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.
回声状态网络（ESN）因其在非线性动力系统建模方面的优越性能而受到越来越多的关注。在传统的回声状态网络模型中，其动态储层（DR）具有随机稀疏的拓扑结构，这在结构和功能上都与真实的生物神经网络相去甚远。为此，我们基于复杂网络理论提出了三种具有新动态储层拓扑结构的新型回声状态网络，分别为具有小世界拓扑结构、无标度拓扑结构和小世界-无标度混合拓扑结构的回声状态网络。然后，我们分析了动态储层结构与其预测能力之间的关系。我们利用两个常用的时间序列来评估三种所提出的回声状态网络的预测性能，并将其与传统模型进行比较。我们还使用独立同分布的时间序列来分析这些回声状态网络的短期记忆和预测精度。此外，我们研究了混合拓扑网络中无标度拓扑和小世界拓扑的比例，并检验了其对回声状态网络性能的影响。我们的仿真结果表明，与传统的回声状态网络模型相比，所提出的回声状态网络模型具有更好的预测能力、更宽的谱半径，但短期记忆能力几乎保持不变。我们还发现，无标度拓扑相对于小世界拓扑的比例越小，记忆能力越好。
