b3443bbf4596d310VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Archived Events/2012-2013 EventsCan Le###@###(Mon, 21 Jan 2013)Can Le###@###(Mon, 21 Jan 2013)438 West HallOptimization via Low-rank Approximation with Application to Network Community Detectionstats135879120000013587912000001:00 PM<p><b>Title: </b>Optimization via Low-rank Approximation with Application to Network Community Detection<br> <b>Advisor:</b> Associate Professor Elizaveta Levina, Professor Roman Vershynin<br> <b>Committee Member: </b>Professor Ji Zhu</p> <p><b>Abstract: </b>The community detection is an important problem in network analysis. Several methods have been proposed to solve the problem, including spectral clustering, modularity, and likelihood-based methods. One issue that most of such methods have to deal with is the optimization problem over a discrete set of labels. In this proposal we introduce a new approach for solving the problem of maximizing the log-likelihood function of the network. By replacing the network adjacency matrix with a low-rank approximation, we reduce the maximization problem over labels to the maximization problem over a convex set in a low-dimensional space. The later problem turns out to have its solution on the boundary and can be solved efficiently. We show that our method performs well over a wide range of parameters. The method may be applied to solve general problems involving functions of adjacency matrices.&nbsp;</p>Njjsantosjjsantos136682922211783443bbf4596d310VgnVCM100000c2b1d38d____once11112newnewEvent Flyer/UMICH/stats/Home/Events/Dissertations and Oral Preliminary Examinations/Can Le PreLim Flyer.pdfCan Le