Obtaining synthetic indications and sorting relevant structures from complex hierarchical clusters of multivariate data

Hierarchical clustering of multivariate data usually provide useful information on the similarity among elements. Unfortunately, the clustering does not immediately suggest the data-governing structure. Moreover, the number of information retrieved by the data clustering can be sometimes so large to make the results little interpretable. This work presents two tools to derive relevant information from a large number of quantitative multivariate data, simply by post-processing the dendrograms resulting from hierarchical clustering. The first tool helps gaining a good insight in the physical relevance of the obtained clusters, i.e. whether the detected families of elements result from true or spurious similarities due to, e.g., experimental uncertainty. The second tool provides a deeper knowledge of the factors governing the distribution of the elements in the multivariate space, that is the determination of the most relevant parameters which affect the similarities among the configurations. These tools are, in particular, suitable to process experimental results to cope with related uncertainties, or to analyse multivariate data resulting from the study of complex or chaotic systems.