RPCA 低秩稀疏分解

针对RPCA（鲁棒pca）的pptPCAPCA直观理解PCA矩阵相乘与投影向量B的模为1,则A与B的内积值等于A向B所在直线投影的矢量长度PCA矩阵相乘与坐标空间映射C三BQB为单位向量,相互正交CCBBPCA月gPCASVD=2OOOOO为单位向量,相互正交PCA前特征前特征前特征iiii出补R:_}原图P与前特征前特征前特征ROBUST PCA经典PCA局限性smc∥ Gaussian noises sparse, large errorsclassical PCA outputclassical PCA outputROBUST PCA提出 Robust pca给出:D=A0+E0,恢复A0和EoLoW-rankSparse componentcomponentgross errorsmin rank(A)+rIEllo subj A+E=D低秩:rank(A)=#{0(A)≠0}sparse, large errors稀疏:‖E|0=#{E;≠0}Not always -original problem is NP-hard