Principal component analysis based on L1-norm maximization

A method of principal component analysis (PCA) based on a new L1-norm optimization technique is proposed. Unlike conventional PCA, which is based on L2-norm, the proposed method is robust to outliers because it utilizes the L1-norm, which is less sensitive to outliers. It is invariant to rotations as well. The proposed L1-norm optimization technique is intuitive, simple, and easy to implement. It is also proven to find a locally maximal solution. The proposed method is applied to several data sets and the performances are compared with those of other conventional methods.