Finally, we performed clustering on the multiscale KNN graph. We used Louvain multilevel community clustering (Blondel et al., 2008). However, modularity-based graph clustering suffers a well-known resolution limit (Fortunato and Barthélemy, 2007), failing to find small clusters even when they are perfectly unambiguously defined. Some variants (so called resolution limit-free algorithms) can be tuned to detect smaller clusters, but at the expense of breaking up large clusters. To circumvent this issue, we exploited the fact that we had both a graph, and an embedding of the graph in two dimensions. We first used Louvain clustering on the graph to find most clusters, and then isolated and re-clustered each cluster using DBSCAN in the low-dimensional space. We call this approach “Polished Louvain.”
