A distance matrix, D ∈ R n×n , is constructed from the pairwise Euclidean distances between points in the synthetic dataset. The cumulative distribution of distances for each point, as shown in Figure , reveals distinct patterns of local and global relationships. Points with sparse local neighborhoods are characterized by initially flat profiles in their cumulative distributions. For example, point A exhibits a large gap between it and its nearest neighbors. Notably, point A's distribution span is relatively compact due to its central Relying on a simple sum or average of distances would overemphasize edge points and neglect the inherent groupings that exist within the data. To address this limitation, we define a notion of influence that weighs neighbors according to a data-driven decay function. In the context of Figure , this is to say that points in the dense cluster in the bottom left corner, tell us little about point B and shouldn't influence its density. As such, we seek to find a cutoff beyond which points do not influence one another.