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

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.