This paper presents a clustering algorithm that is an extension of the
Category Trees algorithm. Category Trees is a clustering method that creates
tree structures that branch on category type and not feature. The development
in this paper is to consider a secondary order of clustering that is not the
category to which the data row belongs, but the tree, representing a single
classifier, that it is eventually clustered with. Each tree branches to store
subsets of other categories, but the rows in those subsets may also be related.
This paper is therefore concerned with looking at that second level of
clustering between the other category subsets, to try to determine if there is
any consistency over it. It is argued that Principal Components may be a
related and reciprocal type of structure, and there is an even bigger question
about the relation between exemplars and principal components, in general. The
theory is demonstrated using the Portugal Forest Fires dataset as a case study.
The distributed nature of that dataset can artificially create the tree
categories and the output criterion can also be determined in an automatic and
arbitrary way, leading to a flexible and dynamic clustering mechanism.