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I have a similarity matrix M - the value M(i,j) indicates the similarity between two elements i and j.

I want to approximate that matrix using a Gaussian Mixture model or I want to cluster that matrix into set of K clusters.

How can I do it? I am not sure about the input of the clustering algorithm.

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Both K-means and GMM need to be able to compute means (centroids), therefore they cannot operate on a given similarit matrix - you need to define a function to compute a mean, and a distance function from the mean. A similarity matrix is not enough (actually, it's useless) for these algorithms.

You can, however,

  • use a clustering algorithm that can work with arbitrary distances / similarities, such as hierarchical linkage clustering, DBSCAN, OPTICS, PAM/k-Medoids
  • use Multidimensional Scaling to approximate your data in an Euclidean vector space, then run other clustering algorithms on the projected data. Interpreting these clusters will be a lot harder though.

You may want to look into advanced clustering frameworks such as ELKI that offer a wide variety of methods. Maybe e.g. subspace clustering or correlation clustering is more appropriate for your problem.

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  • $\begingroup$ Thank you very much for your answer. I have a similarity matrix, how can I get some underlining structure of it? / features from it? may be spectral clustring, etc.?? $\endgroup$ – user570593 Mar 3 '14 at 15:59
  • $\begingroup$ That is the same question again... don't expect clustering to do magic. You will need to experiment, analyze, and try again. $\endgroup$ – Anony-Mousse Mar 3 '14 at 17:35

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