报告名称：A Hybrid Truncated Norm Regularization Method for Matrix Completion

主办单位：英国威廉希尔体育公司

报告专家：李红

专家所在单位：华中科技大学

报告时间：2019年3月22日14:30-15:30

报告地点：英国威廉希尔体育公司201报告厅

专家简介：李红，教授，博士生导师，科技部国际科技合作计划评议专家，湖北省计算数学学会理事，美国IEEE会员。主要从事逼近与计算、机器学习与模式识别等方面的研究，在IEEE Trans等重要学术期刊上发表学术论文50余篇。主持国家自然科学基金、“十二五”航天支撑计划项目及国防预研基金等多个科研项目。2006年至2017年期间多次应邀访问香港浸会大学、澳门大学、美国加州大学尔湾分校（UCI）、澳大利亚悉尼大学等，十余次出席国际学术会议。2006年获宝钢教育基金“优秀教师”奖；2009年主持建设的“复变函数与积分变换”课程被评为国家精品课程，2013年评为国家精品资源共享课程；2013年获湖北省教学成果二等奖；2014年获湖北省名师称号。

报告摘要：Matrix completion has been widely used in image processing, in which the popular approach is to formulate this issue as a general low-rank matrix approximation problem. This paper proposes a novel regularization method referred to as truncated Frobenius norm (TFN), and presents a hybrid truncated norm (HTN) model combining the truncated nuclear norm and truncated Frobenius norm for solving matrix completion problems. To address this model, a simple and effective two step iteration algorithm is designed. Further, an adaptive way of changing the penalty parameter is introduced to reduce the computational cost. Also, the convergence of the proposed method is discussed and proved mathematically. The proposed approach could not only effectively improve the recovery performance but also greatly promote the stability of the model. Meanwhile, the use of this new method can eliminate large variations that exist when estimating complex models, and could achieve great successes in matrix completion. Experiments results on the synthetic data, real-world images as well as recommendation systems, particularly the use of the statistical analysis strategy, verify the effectiveness and superiority of the proposed method, i.e. the proposed method is more stable and effective than other state-of-the-art approaches.