I need some suggestion for clustering (unsupervised classification) method for a consulting project. I am looking for a method that hopefully has the following properties:
The subject of my study has three properties. One is represented by a (non-Euclidean) distance matrix and the other two are in the form of vectors in Euclidean space. The distance matrix comes from sequences and can be in the form of percent of dissimilarity or other measurement of distance of sequences. The algorithm should be able to take both vectors in euclidean space and non-euclidean distance as input. For example, K-medoids can work with a distance matrix but K-means can not.
I would like the algorithm to select the number of clusters and the weight for three properties automatically (with prior knowledge and constraint).
I have information of previously identified “centers of clusters”. I would like to incorporate it as prior or initial values.
As a statistician, I would prefer the method to have a clear likelihood or loss function.
The closest thing I can think of is fitting a mixture model in Bayesian framework using reverse jump MCMC to determine the number of clusters. The vectors in R^d can be easily formulated into a normal likelihood but how to deal with the distance matrix is unclear to me. I can restrict the mean of normal likelihood to be at each of the observation of get the MCMC running but that does not have a clear mathematical / statistical meaning.
Does anyone have experience with a similar problem? Suggestion to references will be highly appreciated!