Exemplars can Reciprocate Principal Components

TL;DR

This paper introduces a novel clustering extension that explores secondary relationships between category subsets, highlighting the potential reciprocal role of exemplars and principal components within an entropy-based classification framework.

Contribution

It extends the Category Trees clustering algorithm to analyze secondary clustering relationships and explores the connection between exemplars and principal components.

Findings

Principal Components may relate reciprocally to exemplars.

The extended clustering method reveals secondary relationships between categories.

The approach is demonstrated on the Portugal Forest Fires dataset.

Abstract

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 Category Trees are then combined with other Self-Organising algorithms from the author and it is suggested that they all belong to the same family type, which is an Entropy-style of classifier.