I have a large number of points in a 2 dimensional space. Each point is assigned to a known cluster. The challenge is to rank the likely hood a new point belongs to each of the clusters.
Simple distance measures (euclidean distance to centre of cluster or sum of distances to points in cluster) are not appropriate as some clusters are localised (small size in x and y), directionally spread ( large size in x or y) or have unusual shapes. Clusters can even overlap to some extent.
What would be an appropriate distance measure to use when ranking clusters for this data point?
In Mplus, you could estimate a mixture model as the first step. As the second step, you could fix all of the parameters to the values found in step 1 and use the new points as data. In this way, you can obtain their posterior probabilities.