Pattern Recognition, 4th Edition

Application to the Mixture Modeling Problem

In this case, the complete data set consists of the joint events (x^k, j^k), k = 1, 2,…, N, and j^k takes integer values in the interval [1, J], and it denotes the mixture from which x^k is generated. Employing our familiar rule, we obtain(2.92)Assuming mutual independence among samples of the data set, the log-likelihood function becomes(2.93)Let P = [P¹, P²,…, P^J]^T. In the current framework, the unknown parameter vector is Θ^T = [θ^T, P^T]^T. Taking the expectation over the unobserved data, conditioned on the ...