Recovering hierarchies in terms of content similarity

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 56; no. 24; pp. 245003 - 245022
• Main Authors: Benatti, Alexandre, F Costa, Luciano da
• Format: Journal Article
• Language: English
• Published: IOP Publishing 16.06.2023
• Subjects: coincidence similarity; hierarchy; reconstructed structures
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/acd3c7

Abstract Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Since the study of these entities often involves sampling (or discovering) the tree nodes in a specific order that may not correspond to the original shape of the tree, reconstruction errors can be obtained. The present work addresses this important problem based on two main resources: (i) the adoption of a simple model of trees, involving a single parameter; and (ii) the use of the coincidence similarity as the means to quantify the errors by comparing the original and reconstructed structures considering the effects of hierarchical structure, nodes content, and uncertainty. Several interesting results are described and discussed, including that the accuracy of hierarchical reconstructions is highly dependent on the values of the uncertainty parameter as well as on the types of trees and that changes in the value of the content parameter can affect the accuracy of reconstructing hierarchies.