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Title: Spectral clustering under degree heterogeneity with the random walk Laplacian Authors:  Alexander Modell - University of Bristol (United Kingdom) [presenting]
Abstract: Community detection on networks often follows a two-step procedure: embedding, in which nodes are represented as points in space, and subsequent clustering. Often, it is of interest to cluster nodes in a way which is agnostic to a degree. We will discuss spectral clustering with the random walk Laplacian matrix, and show that it satisfies this criterion by representing nodes on a projective plane. Theoretical results, such as uniform consistency and a central limit theorem, motivate clustering the embedding using a weighted Gaussian mixture model. Ideas are illustrated using light-hearted examples, such as a network of enmities between characters in the Harry Potter books.