  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.
