<i>R</i>₁-PCA

Principal component analysis (PCA) minimizes the sum of squared errors (L2-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L1-norm PCA (R1-PCA). R1-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the L1-norm PCA. A new subspace iteration algorithm is given to compute R1-PCA efficiently. Experiments on several real-life datasets show R1-PCA can effectively handle outliers. We extend R1-norm to K-means clustering and show that L1-norm K-means leads to poor results while R1-K-means outperforms standard K-means.