学术报告报告题目：EfficientApproaches for Two Big Data Matrix Optimization Problems
报告人：ZhaosongLu教授（西蒙弗雷泽大学）
报告时间：12月22日（星期二）上午10：00
报告地点：4号楼4318室
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数学学院
2015年12月21日
报告摘要：
Inthe first part of this talk, we consider low rank matrix completionproblem, which has wide applications such as collaborative filtering,image inpainting and Microarray data imputation. We present anefficient and scalable algorithm for matrix completion. Ineachiteration, we pursue a rank-one matrix basis generated by the topsingular vector pair of the current approximation residual and updatethe weights for all rank-one matrices obtained up to the currentiteration. We further propose a novel weight updating rule to reducethe time and storage complexity, making the proposed algorithmscalable to large matrices. We establish a linear rate of convergencefor the algorithm. Numerical experiments demonstrate that ouralgorithm is much more efficient than the state-of-the-art algorithmswhile achieving similar or better prediction performance.
Inthe second part we consider the problem of estimating multiplegraphical models simultaneously using the fused lasso penalty, whichencourages adjacent graphs to share similar structures. One importantapplication of this problem is for the analysis of brain networks ofAlzheimer's disease. We establish a necessary and sufficientcondition for the graphs to be decomposable. As a consequence,asimple but effective screening rule is proposed, which decomposeslarge graphs into small subgraphs and dramatically reduces theoverall computational cost. Numerical experiments demonstrate theeffectiveness and efficiency of our proposed approach.