Hybridization of Persistent Homology with Neural Networks for Time-Series Prediction: A Case Study in Wave Height
This is an incremental improvement for researchers and practitioners in oceanography or environmental science needing more accurate wave height predictions.
The paper tackled time-series prediction for wave heights by introducing a feature engineering method using computational topology to enhance neural network models, resulting in significant improvements in R^2 scores and reductions in errors for various network types.
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.