報告題目：Convexity, Sparsity, Nullity and all that … in Machine Learning

主 講 人：Hamid Krim,北卡羅來州立大學教授，IEEE Fellow 

 

報告人簡介：

　　Hamid Krim, 現任美國北卡羅來納州立大學電子與計算機工程系教授，研究興趣為統計信號和圖像分析、應用問題的數學建模。Krim教授曾擔任AT&T貝爾實驗室、麻省理工大學研究專家；曾獲貝爾實驗室杰出成績獎，美國國家科學基金會職業成就獎。目前，Krim是IEEE Transactions on Signal Processing的副主編IEEE Signal Processing Magazine的編委會成員，SPTM和Big Data Initiative的程序委會員會成員，2008年成為IEEE Fellow，被評為2015-2016年IEEE SP Society Distinguished Lecturer。

 

報告摘要：

　　High dimensional data exhibit distinct properties compared to its low dimensional counterpart; this causes a common performance decrease and a formidable computational cost increase of traditional approaches. Novel methodologies are therefore needed to characterize data in high dimensional spaces.

　　Considering the parsimonious degrees of freedom of high dimensional data compared to its dimensionality, we study the union-of-subspaces (UoS) model, as a generalization of thelinear subspace model. The UoS model preserves the simplicity of the linear subspace model, and enjoys the additional ability to address nonlinear data. We show a sufficient condition to use l1 minimization to reveal the underlying UoS structure, and further propose a bi-sparsity model (RoSure) as an effective algorithm, to recover the given data characterized by the UoS model from non-conforming errors/corruptions.

　　As an interesting twist on the related problem of Dictionary Learning Problem, we discuss the sparse null space problem (SNS). Based on linear equality constraint, it first appeared in 1986 and hassince inspired results, such as sparse basis pursuit, we investigate its  relation to the analysis dictionary learning problem, and　show that the SNS problem plays a central role, and may naturally be exploited  to solve dictionary learning problems.

　　Substantiating examples are provided, and the application and performance of these approaches are demonstrated on a wide range of problems, such as face clustering and video segmentation.

 

主持人：歐陽建權教授，湘潭大學信息工程學院副院長

時　間：2017年3月30日下午2：00

地　點：工科樓北樓201

 

歡迎廣大師生參加！

 

湘潭大學信息工程學院

智能計算與信息處理教育部重點實驗室

2017年3月28日