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Abstract
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Graph-structured data is increasingly prevalent across various domains such as social networks, citation networks, biological systems, and recommendation systems. In these applications, accurately identifying patterns and relationships between nodes is crucial for tasks like community detection, anomaly detection, and clustering. Spectral Clustering is a popular technique for graph clustering, leveraging the graph Laplacian to find clusters by minimizing the graph's eigenvalues. However, traditional spectral clustering faces challenges when applied to large-scale or complex datasets, particularly due to issues like over-smoothing, where node representations become too similar, making it difficult to distinguish clusters. Additionally, traditional clustering methods typically focus on a single objective, such as minimizing intra-cluster distance, but real-world applications often require optimizing multiple, competing objectives like cluster cohesion and separation. To address these limitations, integrating Multi-Objective Optimization with Spectral Clustering offers a more nuanced approach, allowing multiple objectives to be optimized simultaneously, leading to more accurate and meaningful cluster assignments. Furthermore, Graphormer, a transformer-based architecture designed for graph-structured data, offers a powerful solution to enhance spectral clustering. By utilizing attention mechanisms, Graphormer learns high-quality node embeddings that capture complex relationships between nodes and edges in large and heterogeneous graphs. This enables more effective clustering, particularly in datasets with intricate graph structures, where traditional spectral clustering methods may struggle. The combination of multi-objective optimization and Graphormer allows for scalable, adaptive clustering solutions that can balance multiple objectives, resulting in better performance for graph clustering tasks. This research is essential for advancing graph clustering techniques, p
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