Navegando por Palavras-chave "Spectral theory"

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    Spectral analysis for anomaly detection in dynamic networks with attributes
    (Universidade Federal de São Paulo, 2023-11-10) Silva, Rodrigo Francisquini da [UNIFESP]; Nascimento, Mariá Cristina Vasconcelos; http://lattes.cnpq.br/1010810293243435; http://lattes.cnpq.br/6809565539156314
    Anomaly detection in diverse datasets is a critical area of research with applicability across a wide range of domains, from cybersecurity, such as in intrusion detection in computer networks, to the financial sector, such as in identifying fraudulent activities in credit card transactions. In scenarios where data can be represented as graphs, graph theory offers a set of metrics and methodologies that are particularly effective in capturing the complex relationships and inherent structures within the data in question. However, anomaly detection in graphs presents a series of intricate challenges that have not yet been fully resolved. One such challenge is the dynamic nature of graphs, which evolve over time, rendering static techniques inadequate. Additionally, the presence of heterogeneous attributes on the vertices and edges of the graph increases the complexity of the problem. Traditional methods often fail to adapt to these temporal and spatial changes and frequently lack the interpretability required for real-world applications. To mitigate these challenges, anomaly detection strategies employing clustering techniques have received increasing attention in the literature. These strategies have the advantage of analyzing clusters or groups of vertices, allowing for a more comprehensive and holistic understanding of the underlying graph structure. Such an approach significantly enhances the method's ability to identify not only isolated anomalies but also anomalies that may be indicative of broader structural issues within the graph. The primary objective of this thesis is to investigate and develop unsupervised strategies for anomaly detection in dynamic graphs that also possess heterogeneous attributes. The proposed strategy aims to identify both structural and contextual anomalies. For the detection of structural anomalies, the analysis focuses on the contribution of vertices to the modularity of a specific network partition. On the other hand, contextual anomalies are identified through the application of spectral operators, such as the Fourier Transform. Computational experiments and case studies using real-world datasets corroborate the efficacy of the proposed method. The results demonstrate that the approach outperforms conventional methods found in the literature in terms of both accuracy and interpretability, making it a significant contribution to the field of anomaly detection in graphs.