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ICML
2006
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R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization

14 years 11 months ago
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
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 R1norm to K-means clustering and show that L1-norm K-means leads to poor results while R1-K-means outperforms standard K-means.
Chris H. Q. Ding, Ding Zhou, Xiaofeng He, Hongyuan
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2006
Where ICML
Authors Chris H. Q. Ding, Ding Zhou, Xiaofeng He, Hongyuan Zha
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