The University of Arizona

Consistency of modularity clustering and Kelvin's tiling problem

Consistency of modularity clustering and Kelvin's tiling problem

Series: Statistics GIDP Colloquium
Location: Math 501
Presenter: Sunder Sethuraman, Department of Mathematics, UA

Given a graph, the popular `modularity' clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this talk, we will discuss consistency properties, or scaling limits, of this method with respect to random geometric graphs constructed from n i.i.d. points, V_n = \{X_1, X_2, . . . ,X_n\}, distributed according to a probability measure supported on a bounded domain in R^d. A main result is the following: Suppose the number of clusters, or partitioning sets of V_n, is bounded above, then we show that the discrete optimal modularity clusterings converge in a specific sense to a continuum partition of the underlying domain, characterized as the solution of a 'soap bubble', or 'Kelvin'-type shape optimization problem

(Refreshments will be served.)

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