Pattern Recognition, 4th Edition

14.2. Mixture Decomposition Schemes

The basic reasoning behind this algorithmic family springs from our familiar Bayesian philosophy. We assume that there are m clusters, C^j, j = 1, …, m, underlying the data set.^[2] Each vector xⁱ, i = 1, …, N, belongs to a cluster C^j with probability P(C^j|xⁱ). A vector xⁱ is appointed to the cluster C^j if

² Recall that the number m is assumed to be known.

The differences from the classification task of Chapter 2 are that (a) no training data with known cluster labeling are available and (b) the a priori probabilities P(C^j) ≡ P^j are not known either. Thus, although the goal is the same, the tools have to be ...