Graph-based clustering has become increasingly significant due to its effectiveness in capturing complex relationships within various data types represented as graphs. This thesis addresses persistent challenges in graph-based clustering methodologies, such as the effective capture of multi-scale structural information, the integration of node features with graph topology, and the interpretability of results. The primary objective of this study is to propose a novel graph-based clustering framework named GraphWave Clustering, which leverages the Adaptive Graph Wavelet Transform (AGWT) along with a simplified graph convolution process to improve clustering outcomes while maintaining scalability and efficiency. The proposed method operates under the premise that real-world networks exhibit intricate structures that can be better understood through multi-scale analysis. The AGWT captures essential features from both the local and global topology of the graph, enabling a more nuanced representation of data points. Additionally, the method fuses these features with node attributes to create an enriched input for subsequent clustering algorithms, primarily employing K-means as a flexible option. Through extensive experimentation on various well-known datasets, including Cora, CiteSeer (ARI: 0.4353, NMI:0.5310, ARI: 0.4406, NMI: 0.4254), PubMed, and Wiki, the efficacy of the GraphWave Clustering framework is empirically validated against state-of-the-art techniques. The results reveal that the proposed algorithm not only enhances clustering accuracy as indicated by metrics such as Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI), but also exhibits improved specificity across most datasets. Notably, it yields competitive results with a considerable degree of robustness across diverse graph structures, particularly excelling in datasets with clear community formations. However, challenges remain in the form of sensitivity to the choice of hyperparameters and potential over-smoothing in feature representation, which may obscure distinct community boundaries. Overall, the GraphWave Clustering framework represents a significant advancement in graph-based clustering methodologies, effectively integrating multi-scale structural insights and node attributes. This research contributes valuable approaches towards addressing the limitations inherent in traditional clustering methods, paving the way for further explorations into adaptive and scalable community detection strategies in complex networked systems. The framework’s versatility sets a foundation for broad applications across various domains, including social network analysis, bioinformatics, and data mining, as well as enabling deeper insights into the structural properties of complex systems.
