Fig. 6: Comparisons on the clustering performance between the local search (LS), Louvain, and density and distance based (DDB) algorithms for two dimensional benchmark vector data.

a represent the network constructed from vector data using the ϵ-ball method (see Supplementary Note 3.1 and Supplementary Fig. 10 for details on the network constructions). b shows the result of the LS method that correctly identify clusters that align with common consensus (see Supplementary Fig. 11 for more cases). In addition, LS can detect noisy points (marked in gray) that are of low degrees but long l_i. c shows the partitions obtained from the Louvain method, which are more fragmented than the LS result (see Supplementary Fig. 13 for more cases). d shows the result obtained from the DDB method which provides correct partitions to most benchmark data, see the original work that introduces DDB¹⁶ for other cases. e–h are the same as (a–d) for another vector dataset, where both a low density manifold and a high density cluster exist. In (h), DDB algorithm fails detecting correct clusters due to its local association rule⁸³ being affected by a mixture of local and global metrics. LS and Louvain methods are performed on the constructed networks shown in (a) and (e), and the DDB algorithm is performed on the original vector data.