Spectra in taxonomic evidence in databases III

Abstract

Numerical Taxonomy aims to group in clusters, using so-called structure analysis of operational taxonomic units (OTUs or taxons or taxa) through numerical methods. These clusters constitute families. Structural analysis, based on their phenotypic characteristics, exhibits the relationships, in terms of degrees of similarity, between two or more OTUs. Entities formed by dynamic domains of attributes, change according to taxonomical requirements: Classification of objects to form families or clusters. Taxonomic objects are here represented by application of the semantics of the Dynamic Relational Database Model. Families of OTUs are obtained employing as tools i) the Euclidean distance and ii) nearest neighbor techniques. Thus taxonomic evidence is gathered so as to quantify the similarity for each pair of OTUs (pair-group method) obtained from the basic data matrix. The main contribution of the present work is to introduce the concept of spectrum of the OTUs, based in the states of their characters. The concept of families’ spectra emerges, if the superposition principle is applied to the spectra of the OTUs, and the groups are delimited through the maximum of the Bienaymé-Tchebycheff relation, that determines Invariants (centroid, variance and radius). Applying the integrated, independent domain technique dynamically to compute the Matrix of Similarity, and, by recourse to an iterative algorithm, families or clusters are obtained. A new taxonomic criterion is thereby formulated. An astronomic application is worked out. The result is a new criterion for the classification of asteroids in the hyperspace of orbital proper elements (the well-known Families of Hirayama). Using an updated database of asteroids we ascertain the robustness of the method. Thus, a new approach to Computational Taxonomy is presented, that has been already employed with reference to Data Mining. The Informatics (Data Mining and Computational Taxonomy), is always the original objective of our researches.