Improving Clustering with Graph Smoothing. - Colley, Charles A. (Tufts Archival Research Center, 2016)
Abstract:Clustering is a data mining technique which offers insight into datasets based offof similarities of elements to each other. Spectral clustering uses decompositionsof matrix representations of graphs to find appropriate clusters in a data set. Inthis thesis we propose two new methods to improve spectral clustering, SmoothedEmbedding clustering and Graph Smoothed clustering which involve perturbing thespectral embedding of a graph and replacing each vertex with a clique respectively.We prove that the process graph smoothing in Graph Smoothing clustering decreasesthe magnitude of the smallest non-zero eigenvalue for a connected weighted graph,and finish with empirical investigation applying to the algorithms to the Fisher Irisdata set.