Hybridization of Persistent Homology with Neural Networks for Time-Series Prediction: A Case Study in Wave Height

TL;DR

This paper presents a novel feature engineering approach using topological data analysis to improve neural network-based time-series predictions of wave heights, significantly enhancing accuracy and reducing errors.

Contribution

It introduces a method that combines persistent homology with neural networks to boost prediction performance in time-series data.

Findings

Significant increase in R^2 scores across models

Notable reduction in maximum errors

Lower mean squared errors achieved

Abstract

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.