If a single link exists between Clusters A and B, they will be linked together at the next stage, even though overall they are dissimilar. This suggests the need for model-based clustering . Mixture Model Clustering A conceptual model for clustering is that the sample comes from a mixture of several populations. This leads to a mathematical probability model for the data called the finite mixture-model. Suppose it is a mixture of two distributions.
Analogous formulas hold for more than two component distributions.
In mixture-model clustering, all parameters are estimated. There is no generally accepted procedure for determining the numer of clusters. This decision should be guided by theory and practicality of the results, along with use of the inter-cluster distances at successive steps. When using a criterion such as between-groups sum of squares or likelihood, this can be plotted against the number k of clusters in a scree diagram. In a mixture-model, the number of parameters, no.parms, is a mean vector for each group, plus the number of elements of the covariance matrix or matrices, plus the number of mixing probabilities.