To demonstrate the efficacy of hierarchical clustering, we performed a comparative benchmark between the conventional empirical clustering approach (outlined in Alg. A.1) and hierarchical clustering (described in Alg. A.2). Across various radius expansions, hierarchical clustering consistently completed within two minutes, indicating significant efficiency. In contrast, the time required for the empirical clustering method increased substantially, from about one minute at a radius of zero to nearly 95 minutes at a radius of three, as shown in .