Low Rank Representation – Theories and Applications(ppt详解).pdf

发布时间：2022-06-09 发布人：admin 分类：说明书资料大小：1.04M 资料格式：pdf 举报版权申诉

tzcwork-4567099-4744302542994336374.pdf-第1页.png

第1页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第2页.png

第2页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第3页.png

第3页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第4页.png

第4页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第5页.png

第5页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第6页.png

第6页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第7页.png

第7页 / 共25页

tzcwork-4567099-4744302542994336374.pdf-第8页.png

第8页 / 共25页

文本预览

Low Rank Representation – Theories and Applications 林宙辰北京大学 April 13, 2012 ¼

Outline • Low Rank Representation • Some Theoretical Analysis • Applications • Generalizations ¼minrank(A);s:t:D=¼(A):

Sparse Subspace Clustering • Sparse Representation • Sparse Subspace Clustering Elhamifar and Vidal. Sparse Subspace Clustering. CVPR2009. minjjxjj0;s:t:y=Ax:(1)minjjzijj0;s:t:xi=X^izi;8i:(2)whereX^i=[x1;¢¢¢;xi¡1;xi+1;¢¢¢;xn].minjjZjj0;s:t:X=XZ;diag(Z)=0:(3)minjjZjj1;s:t:X=XZ;diag(Z)=0:(4)

Sparse Subspace Clustering • Construct a graph • Normalized cut on the graph Elhamifar and Vidal. Sparse Subspace Clustering. CVPR2009. W=(jZ¤j+j(Z¤)Tj)=2

Sparse Subspace Clustering Elhamifar and Vidal. Sparse Subspace Clustering. CVPR2009. Theorem.Assumethedataiscleanandisdrawnfromindependentsubspaces,thenZ¤isblockdiagonal.dim(PiSi)=Pidim(Si):

Drawback of SSC • Sensitive to noise: no cross validation among coefficients Elhamifar and Vidal. Sparse Subspace Clustering. CVPR2009. minjjzijj1;s:t:xi=Xzi;(zi)i=0:(5)minjjZjj1;s:t:X=XZ;diag(Z)=0:(4)

Hints from 2D Sparsity • Rank is a good measure of 2D sparsity – Real data usually lie on low-dim manifolds > 1B dim low-dim subspaces → low rank data matrices – Low rank ↔ high correlation among rows/columns

Low Rank Representation no additional constraint! Liu, Lin, and Yu. Robust Subspace Segmentation by Low-Rank Representation, ICML 2010. minjjZjj1;s:t:X=XZ;diag(Z)=0:(4)minjjZjj¤;s:t:X=XZ:(6)jjZjj¤=Pj¾j(Z),nuclearnorm,aconvexsurrogateofrank.

分享到：

赞收藏

资料库

Low Rank Representation – Theories and Applications(ppt详解).pdf

相关推荐

课程资源

热门标签

最新资料