We derive the clustering problem from first principles showing that the goal of achieving a probabilistic, or "hard", multi class clustering result is equivalent to the algebraic problem of a completely positive factorization under a doubly stochastic constraint. We show that spectral clustering, normalized cuts, kernel K-means and the various normalizations of the associated affinity matrix are particular instances and approximations of this general principle. We propose an efficient algorithm for achieving a completely positive factorization and extend the basic clustering scheme to situations where partial label information is available.
A unifying approach to hard and probabilistic clustering
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 ; 1 ; 294-301 Vol. 1
2005-01-01
400491 byte
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
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