Learning robust principal components from L1-norm maximization

Principal component analysis(PCA) is fundamental in many pattern recognition applications.Much research has been performed to minimize the reconstruction error in L1-norm based reconstruction error minimization(L1-PCA-REM) since conventional L2-norm based PCA(L2-PCA) is sensitive to outliers.Recently,the variance maximization formulation of PCA with L1-norm(L1-PCA-VM) has been proposed,where new greedy and nongreedy solutions are developed.Armed with the gradient ascent perspective for optimization,we show that the L1-PCA-VM formulation is problematic in learning principal components and that only a greedy solution can achieve robustness motivation,which are verified by experiments on synthetic and real-world datasets.