An Analysis of Sea Level Spatial Variability by Topological Indicators and $k$-means Clustering Algorithm

TL;DR

This paper introduces a hybrid clustering approach combining topological data analysis and $k$-means algorithms to improve the categorization of sea level variability patterns across different Malaysian shoreline regions.

Contribution

It presents a novel hybrid method that integrates persistent homology with $k$-means clustering to enhance robustness and accuracy in analyzing sea level data.

Findings

The proposed method outperforms traditional clustering techniques.

Topological information improves classification robustness.

Enhanced categorization of sea level variability patterns.

Abstract

The time-series data of sea level rise and fall contains crucial information on the variability of sea level patterns. Traditional $k$-means clustering is commonly used for categorizing regional variability of sea level, however, its results are not robust against a number of factors. This study analyzed fourteen datasets of monthly sea level in fourteen shoreline regions of Peninsular Malaysia. We applied a hybridization of clustering technique to analyze data categorization and topological data analysis method to enhance the performance of our clustering analysis. Specifically, our approach utilized the persistent homology and $k$-means/$k$-means++ clustering. The fourteen data sets from fourteen tide gauge stations were categorized in classes based on a prior categorization that was determined by topological information, and the probability of data points that belong to certain groups that is yielded by $k$-means/$k$-means++ clustering. Our results demonstrated that our method significantly improves the performance of traditional clustering techniques.