R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization

Authors:
Chris Ding;Ding Zhou;Xiaofeng He;Hongyuan Zha
Affiliations:
Lawrence Berkeley National Laboratory, Berkeley, CA;The Pennsylvania State University, University Park, PA;Lawrence Berkeley National Laboratory, Berkeley, CA;The Pennsylvania State University, University Park, PA
Venue:
ICML '06 Proceedings of the 23rd international conference on Machine learning
Year:
2006

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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.