報(bào)告題目：Convexity, Sparsity, Nullity and all that … in Machine Learning

主 講 人：Hamid Krim,北卡羅來(lái)州立大學(xué)教授，IEEE Fellow 

 

報(bào)告人簡(jiǎn)介：

　　Hamid Krim, 現(xiàn)任美國(guó)北卡羅來(lái)納州立大學(xué)電子與計(jì)算機(jī)工程系教授，研究興趣為統(tǒng)計(jì)信號(hào)和圖像分析、應(yīng)用問(wèn)題的數(shù)學(xué)建模。Krim教授曾擔(dān)任AT&T貝爾實(shí)驗(yàn)室、麻省理工大學(xué)研究專(zhuān)家；曾獲貝爾實(shí)驗(yàn)室杰出成績(jī)獎(jiǎng)，美國(guó)國(guó)家科學(xué)基金會(huì)職業(yè)成就獎(jiǎng)。目前，Krim是IEEE Transactions on Signal Processing的副主編IEEE Signal Processing Magazine的編委會(huì)成員，SPTM和Big Data Initiative的程序委會(huì)員會(huì)成員，2008年成為IEEE Fellow，被評(píng)為2015-2016年IEEE SP Society Distinguished Lecturer。

 

報(bào)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(yáng)建權(quán)教授，湘潭大學(xué)信息工程學(xué)院副院長(zhǎng)

時(shí)　間：2017年3月30日下午2：00

地　點(diǎn)：工科樓北樓201

 

歡迎廣大師生參加！

 

湘潭大學(xué)信息工程學(xué)院

智能計(jì)算與信息處理教育部重點(diǎn)實(shí)驗(yàn)室

2017年3月28日