Dendrograms and irreducible prefix codes

Abstract

Dendrograms have been used in cluster analysis and in hierarchical classification problems. In this paper we note that the Huffman method for producing optimal binary codes also produces only dendrograms.

We define an equivalence relation on codes and give an algorithm to produce a prefix code in each class. We also define minimal and maximal total length functions and by exploiting the relationship between irreducible codes and dendrograms, we derive formulas for them. We also derive a measure of code extensibility.