Extreme learning machine (ELM) allows for fast learning and better generalization performance than conventional gradient-based learning. However, the possible inclusion of non-optimal weight and bias due to random selection and the need for more hidden neurons adversely influence network usability. Further, choosing the optimal number of hidden nodes for a network usually requires intensive human intervention, which may lead to an ill-conditioned situation. In this context, chemical reaction optimization (CRO) is a meta-heuristic paradigm with increased success in a large number of application areas. It is characterized by faster convergence capability and requires fewer tunable parameters. This study develops a learning framework combining the advantages of ELM and CRO, called extreme learning with chemical reaction optimization (ELCRO). ELCRO simultaneously optimizes the weight and bias vector and number of hidden neurons of a single layer feed-forward neural network without compromising prediction accuracy. We evaluate its performance by predicting the daily volatility and closing prices of BSE indices. Additionally, its performance is compared with three other similarly developed models—ELM based on particle swarm optimization, genetic algorithm, and gradient descent—and find the performance of the proposed algorithm superior. Wilcoxon signed-rank and Diebold–Mariano tests are then conducted to verify the statistical significance of the proposed model. Hence, this model can be used as a promising tool for financial forecasting.

中文翻译：

---

用于股票波动预测的化学反应优化极限学习

极限学习机 (ELM) 允许快速学习和比传统的基于梯度的学习更好的泛化性能。然而，由于随机选择和需要更多隐藏神经元而可能包含非最佳权重和偏差，这会对网络可用性产生不利影响。此外，为网络选择最佳隐藏节点数通常需要大量的人工干预，这可能会导致病态情况。在这种情况下，化学反应优化 (CRO) 是一种元启发式范例，在大量应用领域取得了越来越多的成功。它的特点是收敛速度更快，需要的可调参数更少。本研究开发了一个结合 ELM 和 CRO 优势的学习框架，称为化学反应优化的极限学习 (ELCRO)。ELCRO 同时优化单层前馈神经网络的权重和偏置向量以及隐藏神经元的数量，而不会影响预测精度。我们通过预测 BSE 指数的每日波动率和收盘价来评估其表现。此外，将其性能与其他三个类似开发的模型（基于粒子群优化、遗传算法和梯度下降的 ELM）进行比较，发现所提出算法的性能更优。然后进行 Wilcoxon 符号秩和 Diebold-Mariano 检验以验证所提出模型的统计显着性。因此，该模型可以用作财务预测的有前途的工具。