Structure of hierarchic clusterings: implications for information retrieval and for multivariate data analysis

Hierarchic clustering methods may be used to condense information for a user, as they are in multivariate data analysis, or to achieve computational advantages, as they are in information retrieval. The structure of the hierarchic classification produced has a direct bearing on the effectiveness and utility of using cluster analysis, yet this important feature of the classification has only been implicitly referred to in the literature to date. In this study, three different coefficients are defined, each of which quantify the symmetry-asymmetry (balancedness-unbalancedness) of hierarchic clusterings on a scale from 0 to 1. Using examples of data from the areas of information retrieval and of multivariate data analysis, a number of hierarchic clustering methods are discussed in terms of the hierarchies they produce.