Kernel extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has been successfully applied to solve various multivariate time series prediction (MTSP) tasks. Nevertheless, the high-dimensional and nonlinear properties of prediction information against the background of big data bring great challenges to the application of KELM. Recognizing these challenges, this paper develops a KELM-based hybrid MTSP system, aiming to address the effective mining of potential relationships among variables and sample significance. Our system is initiated by devising a feature evaluation mechanism that leverages transfer entropy and directed graph theory, effectively capturing the intricate interactions and intrinsic influences among variables. Next, we introduce a robust local relative density concept to gauge the significance level of different samples in KELM learning, and develop a more efficient KELM. Diverging from previous MTSP methodologies, the developed prediction system is capable of automatically discovering potential relationships between input features and modeling, and simultaneously realizes feature subset selection and modeling learning. Empirical evidence drawn from real-world datasets substantiates the effectiveness and practicality of our proposed system. The results not only validate our approach but also highlight its theoretical and practical superiority over existing state-of-the-art methods.

中文翻译：

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融合转移熵和局部相对密度的混合多元时间序列预测系统


内核极限学习机 （KELM） 作为 ELM 对内核学习的自然扩展，已成功应用于解决各种多变量时间序列预测 （MTSP） 任务。然而，在大数据背景下，预测信息的高维和非线性特性给 KELM 的应用带来了巨大的挑战。认识到这些挑战，本文开发了一种基于 KELM 的混合 MTSP 系统，旨在解决变量之间潜在关系和样本显著性的有效挖掘问题。我们的系统是通过设计一种特征评估机制来启动的，该机制利用转移熵和有向图论，有效地捕获变量之间错综复杂的相互作用和内在影响。接下来，我们引入了一个稳健的局部相对密度概念来衡量 KELM 学习中不同样本的显着性水平，并开发一个更有效的 KELM。与以前的 MTSP 方法不同，开发的预测系统能够自动发现输入特征和建模之间的潜在关系，同时实现特征子集选择和建模学习。从真实世界数据集中提取的经验证据证实了我们提出的系统的有效性和实用性。结果不仅验证了我们的方法，还突出了它相对于现有最先进方法的理论和实践优势。