Music@life
生而知之者,上也。
The highest are those who are born wise.
學而知之者,次也。
Next are those who become wise by learning.
困而學之,又其次也。
After them come those who have to toil painfully in order to acquire learning.
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:
Begin with the disjoint clustering having level L(0) = 0 and sequence number m = 0.
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.
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)]
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)].
If all objects are in one cluster, stop. Else, go to step 2.