用拓扑特征提升神经网络对波高的预测精度
Hybridization of Persistent Homology with Neural Networks for Time-Series Prediction: A Case Study in Wave Height
- 将计算拓扑技术提取的拓扑特征融入神经网络
- 在多个模型上显著提高 $R^2$ 分数并降低误差
- 适合关注时序预测与拓扑数据分析的研究者
时序预测在多个领域持续受到短期与长期因素波动影响的挑战。本文提出一种特征工程方法，利用计算拓扑技术从输入数据中提取有价值的拓扑特征，以提升神经网络模型的预测性能。研究聚焦于波高预测，采用基于拓扑特征的前馈神经网络（FNN）、循环神经网络（RNN）、长短期记忆网络（LSTM）及门控循环单元（GRU）模型。在提前预测任务中，所有模型的 $R^2$ 分数均显著提升，同时最大误差和均方误差也明显下降。
原文摘要 · Abstract (English)
Time-series prediction is an active area of research across various fields, often challenged by the fluctuating influence of short-term and long-term factors. In this study, we introduce a feature engineering method that enhances the predictive performance of neural network models. Specifically, we leverage computational topology techniques to derive valuable topological features from input data, boosting the predictive accuracy of our models. Our focus is on predicting wave heights, utilizing models based on topological features within feedforward neural networks (FNNs), recurrent neural networks (RNNs), long short-term memory networks (LSTM), and RNNs with gated recurrent units (GRU). For time-ahead predictions, the enhancements in $R^2$ score were significant for FNNs, RNNs, LSTM, and GRU models. Additionally, these models also showed significant reductions in maximum errors and mean squared errors.
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