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I am calculating pairwise distances between some points. The obtained distances can either be accurate, over-estimated or under-estimated. The respective probability is 80%, 5% and 15%. And the error range is 50cms.

Ex. For 20 points in 2D space say, A,B,C,D.... I calculate distance between AB, AC, AD, AE..... similarly for all pair of points.

I now need to use these distances to cluster points based on their distances (DBSCAN). But if the distances are not accurately measured, it might lead to incorrect clusters.

So, for clustering, keeping in mind the uncertainty, I need to have a probability density function for the obtained distances for every point object.

Say, if I measure AB = 4.5m. How do I generate a probability function given the three possible outcomes?

How do I model this problem?

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Have a look at uncertain or "fuzzy" DBSCAN.

Kriegel, H. P., & Pfeifle, M. (2005, August). Density-based clustering of uncertain data. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining (pp. 672-677). ACM.

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