*2.4. Initial Values*

Owing to its iterative nature, the EM algorithm can start with either an *E step* or an *M step*. In the context of model-based clustering, initiation with the *M step* takes advantage of the availability of other existing clustering methods, in the sense that, given a data set, we can acquire their initial memberships by first clustering the data with other methods. MCLUST adopts model-based agglomerative hierarchical clustering [7,15] to generate initial memberships. Model-based hierarchical clustering aims at maximizing the *classification likelihood* instead of (5) or (10); at each stage, the maximum-likelihood pair of clusters are merged together. Although the resulting partitions are suboptimal due to its heuristic nature, model-based hierarchical clustering has been shown to often yield reasonable results and is relatively easy to compute [16]. In light of this, we also use model-based hierarchical clustering to obtain initial memberships for MCLUST-ME. For the choice of initial values when starting with *E step* (i.e., initial parameter estimates), see [17] for a nice discussion.
