北航数学论坛

题目: Rank-constrained Inherent Clustering for Multivariate Supervised Learning

报告人：佘轶原 教授（佛罗里达州立大学）

时间：6月26日（星期三）16：00-17：00

地点：主321

摘要：Modern clustering applications are often faced with challenges from high dimensionality, nonconvexity and parameter tuning. This paper gives a mathematical formulation of low-rank clustering and proposes an optimization based inherent clustering framework. The  method  enjoys a nice kernel property to apply to similarity data and can be extended to supervised learning. By use of linearization and block coordinate descent, a simple-to-implement   algorithm is developed, which  performs subspace learning and clustering iteratively. Our non-asymptotic analyses show a tight error rate of   rank constrained inherent clustering and its minimax optimality, along with   a new information criterion  for parameter tuning in jointly rank-deficient and equi-sparse models. These results are the first of their kind in multivariate supervised learning and show interesting differences  from those obtained for supervised learning with sparsity.   Extensive simulations and real-data experiments demonstrate the excellent performance of the proposed approach.

报告人简介：佘轶原，佛罗里达州立大学教授。2008年获得斯坦福大学统计学博士学位,自2008年起任职于佛罗里达州立大学统计系，曾获得  NSF CAREER Award，Florida State University Developing Scholar Award 等奖项。佘教授担任  Metrika ，IEEE Transactions on Network Science and Engineering 以及Journal of the American Statistical Association等顶级杂志的编委。他的主要研究方向包括：高维统计、统计机器学习、优化、信号处理、稳健统计和网络科学等领域。

邀请人：陈迪荣