A ranked linear assignment approach to Bayesian classification

We derive the averaged permutation matrix representation over Sn, given the mean of M data vector samples. This matrix turns out to be a doubly stochastic matrix,PM, whose (i,j) element is the probability that data stream component i corresponds to class j, given the sample mean vector XM. We prove that PM converges to ϕ in probability. Moreover, it is shown that PM can be accurately approximated by extending from the solution of the classical linear assignment problem of finding the permutation with maximum likelihood to the solution of the ranked linear assignment problem in which a small number of permutations with rapidly decreasing likelihoods are identified.