Exploring Complex Networks: Matrix-based and Multiscale Approaches for Pattern Recognition - Neiva, Mariane Barros (2023)
Complex networks are essential tools for understanding interconnected systems across various domains. This thesis focuses on the analysis, classification, and modeling of complex networks, aiming to extract meaningful insights using innovative methodologies. The study explores the complex network classification, with a secondary focus on modeling real phenomena in health science and shape analysis. The research objective is to develop novel methodologies surpassing existing network classification techniques. Two key components are investigated: utilizing the adjacency matrix for network analysis and applying multiscale techniques for graph analysis. The investigation of the graph matrices reveals promising results, with node centrality-based ordination and node similarity enhancing image analysis representation. Quantitative analysis on diverse datasets, including real systems, demonstrates satisfactory classification accuracies with low parametrization. Also, computer vision-inspired techniques, such as k-core decomposition and distance transform enhance graph and shape classification. The completion of this PhD in complex networks also explores the ICD-ORPHA network from the Brazilian Ministry of Health. To address the limitations of the ICD-10 system for rare diseases, a specialized medical terminology known as ORPHA is employed, providing a comprehensive nomenclature specifically designed for rare diseases. This research expands the understanding of complex network modeling and its application in the healthcare domain through an interactive web-app system. Furthermore, during the COVID-19 pandemic, a proposed SIR-based model evaluates population dynamics and enhances understanding of the evolution of the pandemic. These methodologies offer valuable tools for public health insights and classification performance improvement. In conclusion, this research advances complex network analysis, classification, and modeling with innovative methodologies. Findings have broad applications across domains, including synthetic and real networks, health data, and shape analysis. The research outcomes offer practical solutions for understanding interconnected systems and contribute to the advancement of complex network analysis.