I have a dataset of about 53000 points. It has been clustered twice, based on two sets of unrelated attributes. For the first clustering (clustering 1) I used DBScan, and it ended up with about 700 clusters, with 30000 of the points being labeled as noise. Then, on another set of attributes, I clustered them using kmeans, which resulted in 5 different attributes (clustering 2).
However, I have a feeling the two sets of attributes may have some relation after all. Therefore, I want to measure how variable the points are in terms of cluster membership of clustering 2 within each cluster of clustering 1. I don't have a strong mathematical background, I've tried simply calculating the SD within each clustering 1 group, but this does not work since the cluster labels are of influence (a group with 50% in cluster 0 and 50% in cluster 1 will have different results than a group with 50% in cluster 0 and 50% in cluster 2)
Unfortunately I cannot share my data, but I have included a screenshot, I hope that clarifies what I mean.