学术报告 报告题目：Efficient Approaches for Two Big Data Matrix Optimization Problems
报 告 人：Zhaosong Lu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：
In the first part of this talk, we consider low rank matrix completion problem, which has wide applications such as collaborative filtering, image inpainting and Microarray data imputation. We present an efficient and scalable algorithm for matrix completion. In eachiteration, we pursue a rank-one matrix basis generated by the top singular vector pair of the current approximation residual and update the weights for all rank-one matrices obtained up to the current iteration. We further propose a novel weight updating rule to reduce the time and storage complexity, making the proposed algorithm scalable to large matrices. We establish a linear rate of convergence for the algorithm. Numerical experiments demonstrate that our algorithm is much more efficient than the state-of-the-art algorithms while achieving similar or better prediction performance.
In the second part we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. One important application of this problem is for the analysis of brain networks of Alzheimer's disease. We establish a necessary and sufficient condition for the graphs to be decomposable. As a consequence,a simple but effective screening rule is proposed, which decomposes large graphs into small subgraphs and dramatically reduces the overall computational cost. Numerical experiments demonstrate the effectiveness and efficiency of our proposed approach.