# 12.3.4 Class overlap statistics

We focus here on the three classifiers providing results in the extragalactic tables. For each of them, it is interesting to check the distribution of the respective classes reported in the tables, both among the other modules, and against the other classes of a given classifier (DSC, Vari-Classification and OA). For the former checks, we consider neither the Vari-Agn sample as it is a sub-sample of Vari-Classification, nor the OA sample as it is not used to build the source list. For the latter checks, statistics can be extracted for each pair of classifier. In the following, the class labels reported correspond to those hosted by the classlabel_dsc, vari_best_class_name and classlabel_oa fields. It should also be noted that the respective classifiers can provide different classification and as such their quasar and galaxy labels do not necessarily agree.

## qso_candidates table

### DSC classes against other QSO modules

Table 12.7 shows the overlap between the various QSO modules and the DSC ‘Combmod’ classes. As can be seen, for all modules, the majority of sources overlapping with DSC are classified as quasars, with a minimum of nearly 80% for any module other than QSOC. This confirms the high completeness level of the DSC quasar sample. Non-surprisingly, the next most significant contributing class is that of ‘star’, which accounts of more than 1/3 of the QSOC overlaps. Also, overlaps with the galaxy class are relatively limited.

The same statistics using this time the classes from the DSC-Joint classification are shown in Table 12.8. Owing to the majority of DSC-Joint sources being classified as ‘unclassified’, the overall number of sources from the various modules overlapping with the DSC-Joint quasar class drops significantly. However, the relative fraction of sources from a given module overlapping with the DSC-Joint quasar class is higher compared to that of the full DSC sample (Table 12.7).

### Vari-Classification classes against other QSO modules

We describe here the overlaps between the various classes featured in the qso_candidates table from the Vari-Classification. By construct the majority of those correspond to the ‘AGN’ class, but other classes also enter the table via sources contributed by the other modules (see the vari_classifier_class_definition table for a definition of the codes used for these classes). Table 12.9 shows their distribution among the various QSO modules, showing that about 8% of all sources featuring such classification are not labelled as ‘AGN’. Of those, the majority (5% of the total) are labelled as RR Lyrae, which indeed is a variable type known to be mistaken as extragalactic sources in variability studies (Rimoldini et al. 2022). The overlap of the ‘AGN’ class with other modules does not exceed half of the sources from those modules, but this is because the majority of the remaining sources do not overlap with the Vari-Classification. In effect, nearly all of the sources in common are labelled as ‘AGN’, showing that this sample is very pure but also achieves a good completeness especially against the CRF3 and the Surface brightness sample.

### Outlier Analysis classes against other QSO modules

The OA classes featured in the qso_candidates table are here checked against the sources from the other QSO modules. It should be borne in mind here that OA entries in this table are not based on any selection specific to the OA classes, instead the OA information is simply populated for all sources being selected as eligible by the other modules.

As explained in Section 11.3.12, several OA classes can be associated with quasar classification because separate classes are used for different redshift intervals. To simplify the analysis, we group them here in some sort of meta-classes gathering all sources of a certain source type. We isolate here four meta-classes: Quasar, Galaxy, White Dwarf, and any other star category different from White Dwarf. The distribution of the 2.8 million OA sources featured in qso_candidates over these meta-classes is shown in the second column of Table 12.10.

### Outlier Analysis classes against DSC and Vari-Classification classes

We check here how the OA classes compare to those of the respective DSC and Vari-Classification classes compare for the sources present in the qso_candidates table. We use the same meta-class scheme as above to organise the OA class labels. Table 12.11 and Table 12.12 shows the corresponding class overlaps.

Owing to the selection rules applied to build the DSC sample in the qso_candidates table, this comparison has several biases and is not necessarily representative of the effective classification performance of OA. On the one hand there is a selection bias in that most of the sources featuring DSC results in the qso_candidates tables are selected based on their quasar class, and 80% of the DSC sources end up having this class in the table. On the other hand, as illustrated e.g. in Figure 12.7, it is expected that a large part of the DSC sources are in fact stellar. With these limitations in mind, the agreement regarding classification as quasar appears to be good, with two third of the OA objects classified as quasar having the same label in DSC. This is less so for the other OA classes, whereby the DSC quasar class is also the one most assigned, probably for the reasons explained here. Concerning the comparison with the Vari-Classification, the largest source overlap corresponds to a match between the ‘AGN’ and the OA quasar classes (55% of the OA sources matched to the ‘AGN’ class). A full overview of the OA classification results is given in Section 11.3.12.

## galaxy_candidates table

### DSC classes against other Galaxy modules

Table 12.13 shows the overlapsOverlaps between between the various Galaxy modules and the DSC ‘Combmod’ classes. The formatting is the same as that used for the corresponding quasar table in Table 12.7.

Again, the majority of the sources of a given module overlap with the DSC ‘Combmod’ galaxy class, although the corresponding fractions are not as high as for the quasar modules, and do not exceed about 2/3 of the samples based on Surface brightness or Vari-Classification analyses. The overlap with UGC is very high simply because of the way UGC sources are selected (see Section 11.3.13). The rest of the sources are mostly labelled as stars, and a small fraction appear as quasar.

Similar to the quasar sample, Table 12.14 shows the same overlap matrix using this time the classes from the DSC-Joint sample in the galaxy_candidates table.

### Vari-Classification classes against other Galaxy modules

Similar to Table 12.9, one can check the distribution of the various classes assigned by the Vari-Classification analysis against the other Galaxy modules. This is summarised in Table 12.15, showing that only a small fraction of sources are labelled differently from ‘GALAXY’, and that they essentially correspond to sources labelled as ‘AGN’. Again, essentially all sources overlapping with the other Galaxy modules are labelled as ‘GALAXY’, and their completeness level against these modules varies between $\sim$40% and 70%.

### Outlier Analysis classes against other Galaxy modules

The same analysis as that shown in Table 12.10 is illustrated in Table 12.16, using the same meta-classes.

Unlike for the qso_candidates table, the majority of the OA sources featured in the galaxy_candidates table are labelled as galaxy following our OA meta-class scheme. Also, nearly all of the sources in common with the other Galaxy modules are labelled as galaxy according to this scheme, indicating a good performance of the OA clustering for that particular class. The apparent completeness against DSC or UGC is poor, but this is likely rather due to the large amount of stellar contamination in these samples.

### Outlier Analysis classes against DSC and Vari-Classification classes

Similar to what is shown in Table 12.11 and Table 12.12, we check here how the OA classes compare to those of the respective DSC ‘Combmod’ and Vari-Classification classes compare for the sources present in the galaxy_candidates table. We use the same meta-class scheme as above to organise the OA class labels. Table 12.17 and Table 12.18 compile the corresponding source overlaps. Overall, the match between the OA Galaxy class and the corresponding galaxy classes of DSC and Vari-Classification is better than the equivalent for the quasar class: 90% (respectively 99%) of OA source matches to the DSC ‘galaxy’ class (respectively Vari-Classification ‘GALAXY’ class) correspond to the OA Galaxy class.