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Item Hierarchical fuzzy spectral clustering in campaign finance social networks(Montana State University - Bozeman, College of Engineering, 2021) Wahl, Scott Allen; Chairperson, Graduate Committee: John SheppardCommunity detection in networks is an important tool in understanding complex systems. Finding these communities in complex real-world systems is important in many disciplines, such as computer science, sociology, biology, and others. In this research, we develop an algorithm for performing hierarchical fuzzy spectral clustering. The clustering algorithm is applied to small benchmark problems, as well as a large real-world campaign finance network. Afterwards, we extend the hierarchical fuzzy spectral clustering for use in evolving networks. The discovered communities are tracked through the evolving network and their underlying properties analyzed. Third, we apply association rule mining on community-based partitions of the data. A comparison of the results within and between communities show the effectiveness of this method for adding interpretability to the underlying system. Fourth, we examine the ability of hierarchical fuzzy spectral clustering on a graph to predict behavior that is not present in the graph itself. The results are shown to be effective in predicting votes in the United States legislature based on the campaign finance networks. Finally, we develop an orthogonal spectral autoencoder that is used to perform graph embedding. This approximation model avoids the eigenvector decomposition of the full network, as well as allows out-of-sample spectral clustering. The results show the embedding performs comparably to the full spectral clustering.