Clustering-based Sampling and Regularization Techniques for Enhanced Graph Signal Reconstruction

Graph Signal Processing (GSP) has become an essential framework for analyzing data defined over graphs, such as those found in sensor networks and social media. A critical challenge in GSP is the reconstruction of signals at all nodes from a limited number of measurements, especially when collecting data from every node is impractical due to constraints like energy consumption and bandwidth limitations. This paper presents a novel approach that combines clustering-based sampling with regularization techniques to enhance graph signal reconstruction. By applying clustering algorithms, we effectively select representative nodes that capture the diverse characteristics of the graph while minimizing redundancy. We then formulate the reconstruction problem as an optimization task that incorporates regularization to improve robustness against noise and missing data. Our methodology is validated through comprehensive numerical simulations conducted on various graph structures, including small-world and scale-free networks. The results demonstrate that our approach significantly improves reconstruction accuracy compared to traditional sampling methods. This work not only advances the field of graph signal processing but also provides practical insights for applications in environmental monitoring, social network analysis, and beyond.