Music@life

Algorithm

The following algorithm is an agglomerative scheme that erases rows and columns in a proximity matrix as old clusters are merged into new ones. The proximity matrix D contains all distances d(i,j). The clusterings are assigned sequence numbers 0,1,......, (n − 1) and L(k) is the level of the kth clustering. A cluster with sequence number m is denoted (m) and the proximity between clusters (r) and (s) is denoted d[(r),(s)].

The algorithm is composed of the following steps:

1. Begin with the disjoint clustering having level L(0) = 0 and sequence number m = 0.
2. Find the most similar pair of clusters in the current clustering, say pair (r), (s), according to d[(r),(s)] = min d[(i),(j)] where the minimum is over all pairs of clusters in the current clustering.
3. Increment the sequence number: m = m + 1. Merge clusters (r) and (s) into a single cluster to form the next clustering m. Set the level of this clustering to L(m) = d[(r),(s)]
4. Update the proximity matrix, D, by deleting the rows and columns corresponding to clusters (r) and (s) and adding a row and column corresponding to the newly formed cluster. The proximity between the new cluster, denoted (r,s) and old cluster (k) is defined as d[(k), (r,s)] = min d[(k),(r)], d[(k),(s)].
5. If all objects are in one cluster, stop. Else, go to step 2.