FDR (Miller et al. 2001) with an $\alpha=0.2$ ([*i.e.*]{}, only allowing a false discovery rate of 20%), a threshold in probability is determined that corresponds to galaxies that possess a high count of nearest neighbors in their 7–dimensional box.

    ![The projected galaxy distribution in the simulations before (left) and after (right) the C4 algorithm have been run and a threshold applied to eliminate field-like galaxies. This illustrates the effect of Step 6 in the algorithm.[]{data-label="before"}](before_after.ps){width="10cm"}

6.  All galaxies in our sample below this threshold in probability are removed, which results in the eradication $\simeq80\%$ of all galaxies. By design, the galaxies that are removed are preferentially in low density regions of this 7–dimensional space ([*i.e.*]{}, the field population). The galaxies that remain are called “C4 galaxies” which, by design, reside in high density regions with neighboring galaxies that possess the same colors as the target galaxy. Figure \[before\] illustrates this step

7.  Using only the C4 galaxies, the local density of all the C4 galaxies is determined using the distance to the $8^{th}$ nearest neighbor.

8.  The galaxies are rank order based on these measured densities and then assigned to clusters based on this ranked list. This is the same 