R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
Proceedings of the 23rd international conference on Machine learning - ICML '06, volume 148 of ACM International Conference Proceeding Series, page 281-288. ACM, (2006)DOI: 10.1145/1143844.1143880
Abstract
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.
