10.4.3 Four-dimensional clustering test

We consider here 4D subspaces always featuring ra, dec and two of all astrometric and photometric observables and their associated uncertainties and correlations. For all patches, the subspaces that systematically show the largest degree of clustering are those spanned by a parameter related to the number of astrometric or photometric observations, such as phot_g_n_obs, matched_observations, astrometric_n_good_obs_al. We once again find ‘patch-a’ and ‘patch-d’ to show similar properties as regions with, on average, a higher number of astrometric and photometric observations. The same is true for ‘patch-b’ and ‘patch-c’. This indicates that the patterns present in the sky are directly related to number of transits in the field. This is further confirmed by the fact that the KLD values obtained in 4D (ra, dec + 2 observables) are larger than for the 2D cases encompassing the same subset of observables.

When we apply this test on the data from the different subsets listed in Table 10.5, we recover the results from the three-dimensional KLD test. We find that the data from the filters DUPVISA and DUPMATA appears to be clustered the least. Also, as before, we find the data to be more clustered for brighter stars.