Pattern Recognition, 4th Edition

Comparison of P with a Clustering C

In this case, C may be either a specific hierarchy of clusterings or a specific clustering. The latter may be produced either by cutting the dendrogram produced by a hierarchical algorithm at a given level (see Chapter 13) or by any other algorithm discussed in the previous chapters. However, a prespecified hierarchy of partitions is rarely available in practice. Thus, the problem of validating hierarchies of clusterings is of limited practical interest.

In the sequel, we consider the validation task concerning a clustering, C, resulting from a specific clustering algorithm, in terms of an independently drawn partition P of X. Let C = {C¹,…,C^m} and P = {P¹,…,P^s}. Note that the number of clusters in C need ...