学术报告： Efficient Approaches for Two Big Data Matrix Optimization Problems
Abstract: 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 each iteration, 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.
报告人：Zhaosong Lu, Ph.D.，Associate Professor of Operations Research，Simon Fraser University，在SIAM Journal on Optimization、Mathematical Programming、SIAM Journal on Scientific Computing等顶级杂志发表论文20余篇，现为
• Associate Editor: SIAM Journal on Optimization.
• Associate Editor: Big Data and Information Analytics.