Graph optimization in graph signal processing - Pei, Jingxiang (Nanyang Technological University, 2025)
With the rapid development of big data and complex networks, traditional data processing is unable to meet the demand. Therefore, graph signal processing is gradually receiving attention from researchers. This method extends traditional signal processing theory to graph network structures and provides an effective tool for graph signal processing. This article is based on monthly average temperature data from 10 major cities in China to study graph optimization tasks and achieve graph smoothing based on observed graph signals. The article first outlines the basic theoretical framework of graph signal processing and summarizes its applications in social, sensor, infectious disease and transportation networks. Subsequently, Pearson correlation similarity and Gaussian kernel between cities is calculated and graph structure is optimized by neighbor aggregation and gradient descent algorithms. Finally, factor analysis is introduced to optimize latent variables, and genetic algorithm is used to optimize graph structure. The experimental results indicate that the optimized graph structure can effectively capture certain climate related features between cities. The graph structure can reflect actual physical correlations and also has graph signal smoothness. But some of the results deviate from climatological expectations. In this dissertation, issues were discussed, and improvement strategies were proposed for data and model structure.