# Cluster confidence scoring

I have a scenario where I am provided a list of clusters and pairwise distance only between items in same cluster. I need to rank these clusters based on some kind of relative score from this info.

e.g. a if [A,B,C] is a given cluster, then I have d(A,B), d(B,C) and d(C,A), where d is their distances. However, I do not have the distance of A or B or C with points belonging to other clusters.

I was thinking of ranking the clusters based on ascending order of median value of inside-cluster pairwise-distances after computing this median value for all clusters. Please let me know if there is any other ideas or major drawback in the current approach. In my scenario it is fine if the inter clusters distances are not optimized because the goal is to rank given clusters with some kind of relative confidence score

NOTE: I also have an information that if d(X,Y) for any point X and Y is < 5, then they are meant to be in the same cluster, else it is an incorrect assignment. It is also a possibility that X,Y,Z share the same cluster because d(X,Y) <5 and d(Y,Z) < 5 but d(Z,X) may NOT be <5, they share the same cluster because of linkage between (X,Y) and (Y,Z).I have a scenario where I am provided a list of clusters and pairwise distance only between items in same cluster. I need to rank these clusters based on some kind of relative score from this info.

e.g. a if [A,B,C] is a given cluster, then I have d(A,B), d(B,C) and d(C,A), where d is their distances. However, I do not have distance of A or B or C with points belonging to other clusters.

I was thinking of ranking the clusters based on ascending order of median value of inside-cluster pairwise-distances after computing this median value for all clusters. Please let me know if there is any other ideas or major drawback in the current approach. In my scenario, it is fine if the inter-clusters distances are not optimized because the goal is to rank given clusters with some kind of relative confidence score

NOTE: I also have a piece of information that if d(X, Y) for any point X and Y is < 5, then they are meant to be in the same cluster, else it is an incorrect assignment. It is also a possibility that X, Y, Z share the same cluster because d(X, Y) <5 and d(Y, Z) < 5 but d(Z, X) may NOT be <5, they share the same cluster because of linkage between (X, Y) and (Y, Z).