学 术 报 告

题 目：A sparse group lasso convex clustering and its fast optimization

algorithm

报 告 人：孔令臣 教授 北京交通大学

主 持 人：杨 辉 教授 贵州大学

时 间：2019年10月18日16:30-17:30

地 点：博学楼416-1 / 数学与统计学院会议室

报告摘要：Cluster analysis is an important ingredient of unsupervised learning, and the classical clustering methods include K-means clustering, spectral clustering etc. These methods may get stuck in local optimal solutions due to the involved nonconvex optimization model. Recently, convex clustering has attracted a significant interest because its global optimal solution can be found easier than classical clustering methods. However, in high-dimensional scenarios, the performance of convex clustering is unsatisfactory because some noninformative features are included in the clustering. In this paper, considering the special structure of data, we propose a sparse group lasso convex clustering of high-dimensional data. And we prove that the proposed estimation has desirable statistical properties, including the finite sample bound for prediction error and feature screening consistency. Furthermore, we design a powerful semi-proximal alternating direction method of multipliers to solve the sparse group lasso convex clustering, and its convergence analysis is established without any conditions. Finally, the effectiveness of the proposed method is well demonstrated on synthetic and real datasets.

报告人简介：孔令臣，北京交通大学理学院教授，博士生导师，中国运筹学会数学规划分会副秘书长。2007年毕业于北京交通大学，获博士学位。2007-2009年，赴加拿大滑铁卢大学组合与优化系从事博士后研究。2009年9月入职北京交通大学数学系，2010年晋升为副教授，2014年晋升为教授，曾受邀访问新加坡国立大学数学系、美国明尼苏达大学统计系、香港中文大学数学系等著名科研院所。主要从事优化与统计学习、高维统计分析、稀疏优化、对称锥互补和优化问题以及医学成像等方面的研究。主持国家自然科学基金面上项目2项、留学回国人员项目1项和多项北京市科研项目，参与973项目、国家自然科学基金重点项目、北京市自然科学基金重点项目等科研课题。在Mathematical Programming，SIAM J. Optimization、Computational Optimization & Applications、Journal of Optimization and Application、Statistica Sinica、计算数学、数学进展等国际国内杂志发表学术论文30余篇。获得2012度中国运筹学会运筹青年奖。

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