NC N macro itemList(s)

N-cluster the states listed in the itemList and tie each cluster i as macro macroi where i is 1,2,3,...,N. The set of states in the itemList are divided into N clusters using the following furthest neighbour hierarchical cluster algorithm:

         create 1 cluster for each state;
         n = number of clusters;
         while (n>N) {
            find i and j for which g(i,j) is minimum;
            merge clusters i and j;
         }

Here g(i,j) is the inter-group distance between clusters i and j defined as the maximum distance between any state in cluster i and any state in cluster j. The calculation of the inter-state distance depends on the type of HMMs involved. Single mixture Gaussians use

where is the dimensionality of stream s. Fully tied mixture systems (ie TIEDHS) use

and all others use

where is as defined in equation 7.1 for the continuous case and equation 7.3 for the discrete case. The actual tying of the states in each cluster is performed exactly as for the Tie (TI) command below. The macro for the i'th tied cluster is called macroi.