利用聚类回声状态网络进行多变量时间序列预测
Multivariate time series prediction using clustered echo state network
AI总结：
本文提出了一种聚类回声状态网络（CESNs），通过将 reservoir 节点划分为集群来提升多变量时间序列的预测能力，实验表明其在预测精度和抗噪声能力上优于传统 ESNs。
摘要：
许多自然和物理过程可以通过分析多个系统变量的演变来理解，形成多变量时间序列。预测此类时间序列具有挑战性，因为变量之间存在固有的噪声和相互依赖性。回声状态网络（ESN）是一种递归计算（RC）模型的类别，通过仅训练输出权重而固定 reservoir 动力学，为传统循环神经网络提供了一种高效替代方案。我们提出了一种聚类 ESNs（CESNs），通过将 reservoir 节点划分为集群，每个集群对应一个不同的输入变量，从而增强对多变量时间序列的建模和预测能力。输入信号直接映射到其对应的集群，集群内连接保持密集，而集群间连接稀疏，模仿生物神经网络的模块化架构。这种架构通过限制跨变量干扰来提高信息处理能力，并通过通过岭回归进行独立集群训练来提高计算效率。我们进一步探讨了不同的 reservoir 拓扑结构，包括环形、Erdős-Rényi（ER）和无标度（SF）网络，以评估其对预测性能的影响。我们的算法在多样化的现实世界数据集上表现良好，如股票市场、太阳风和混沌 Rössler 系统，证明了 CESNs 在预测准确性和对噪声的鲁棒性方面始终优于传统 ESNs，特别是在使用 ER 和 SF 拓扑结构时。这些发现突显了 CESNs 在复杂多变量时间序列预测中的适应性。
英文摘要：
Many natural and physical processes can be understood by analyzing multiple system variables evolving, forming a multivariate time series. Predicting such time series is challenging due to the inherent noise and interdependencies among variables. Echo state networks (ESNs), a class of Reservoir Computing (RC) models, offer an efficient alternative to conventional recurrent neural networks by training only the output weights while keeping the reservoir dynamics fixed, reducing computational complexity. We propose a clustered ESNs (CESNs) that enhances the ability to model and predict multivariate time series by organizing the reservoir nodes into clusters, each corresponding to a distinct input variable. Input signals are directly mapped to their associated clusters, and intra-cluster connections remain dense while inter-cluster connections are sparse, mimicking the modular architecture of biological neural networks. This architecture improves information processing by limiting cross-variable interference and enhances computational efficiency through independent cluster-wise training via ridge regression. We further explore different reservoir topologies, including ring, Erdős-Rényi (ER), and scale-free (SF) networks, to evaluate their impact predictive performance. Our algorithm works well across diverse real-world datasets such as the stock market, solar wind, and chaotic Rössler system, demonstrating that CESNs consistently outperform conventional ESNs in terms of predictive accuracy and robustness to noise, particularly when using ER and SF topologies. These findings highlight the adaptability of CESNs for complex, multivariate time series forecasting.
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