Detecting Hierarchical Clusters and Estimating their Modularity Directly from Dendrograms

Abstract

Identifying possible clusters in datasets and estimating their hierarchical modularity are central tasks in pattern recognition. In the present work, concepts and methodologies are described for performing these tasks while considering only the density of mergings obtained from hierarchical representations (dendrograms) of data inter-relationship along a scale variable. More specifically, the mergings of subclusters along the scale variable are obtained, yielding a respective merging density function. After this function is balanced along the scale variable, peak detection is applied in order to estimate, within a specified resolution, the respective hierarchical clusters and their hierarchical modularity. The potential of the reported approach is illustrated for some types of data and dendrograms, and the possibility of recursive cluster detection is also considered.