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Lundi 15 mai 2017

Intervenant : Jiashun JIN (Carnegie Mellon University)

« Estimating network memberships by mixed-SCORE » 

De 15h à 16h15, en salle 08 à l'ENSAE : 3, avenue Pierre Larousse à Malakoff (Tram T3 : arrêt « Porte de Vanves » ou Métro - ligne 13 station  : « Porte de Vanves » ou « Malakoff Plateau de Vanves »)

Consider an undirected mixed membership network with n nodes and K communities. For each node i from 1 to n, we model the membership by a Probability Mass Function (PMF) Pi = (Pi(1), Pi(2), ..., Pi(K))', where Pi(k) is the probability that node i belongs to community k, k from 1 to K. We call node i "pure" if Pi is degenerate and "mixed" otherwise. The primary interest is to estimate Pi. We model the adjacency matrix A with a Degree Corrected Mixed Membership (DCMM) model. Let xi_1, xi_2, ... , xi_K be the K leading eigenvectors of A. We denote R in R^{n;K-1} by the matrix of entry-wise eigen-ratios where R (i; k) = xi_{k+1}(i)/xi_1(i), k from 1 to K-1, i from 1 to n. We reveal an interesting phenomenon: if we view each row of R as a point in R^{K-1}, then the rows illustrate the silhouette of a simplex, where a row corresponding to a pure node falls close to one of the K-vertices, and other rows approximately fall in the interior of the simplex. The simplex structure inspires a new approach to estimating the memberships which we call the Mixed-SCORE, and at the heart of the method is an easy-to-use Vertex Hunting algorithm. The approach is successfully applied to 4 network data sets with encouraging results. We explain that the simplex structure is real and not coincidental, and study the convergence rate of Mixed-SCORE.

Ce séminaire est organisé par :

Alexandre TSYBAKOV         (Laboratoire de Statistique-CREST)

Cristina BUTUCEA                (Laboratoire de Statistique-CREST)