Hybridizing persistent homology and machine learning for oceanographic time series

ABSTRACT Oceanographic phenomena are inherently complex due to factors such as global warming, ice melting, and human activities. Analyzing oceanographic data presents a challenging task, and a quantitative approach is often implemented to address these complexities. Traditional machine learning techniques, such as regression and cluster analysis, are commonly employed for predicting and identifying similarities in oceanographic conditions across different locations. This study explores the integration of qualitative approaches into oceanographic data analysis by developing hybrid models that combine topological data analysis (TDA) with traditional machine learning methods. The focus is on extracting qualitative features using persistent homology, the core tool of TDA, and incorporating these features into machine learning models such as support vector regression (SVR) and hierarchical clustering analysis (HCA). The study applies these methods to the following two oceanographic datasets: wave height data from buoy stations in Canada and sea level data from gauge stations in Japan. The results show that the hybrid models significantly outperform traditional approaches across several performance metrics, including the R2 score, maximum absolute error, mean squared error, and Rand score. This demonstrates the value of adding topological information to machine learning models, which enhances their predictive performance.