We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix M\u0003, where (1 – cx\u000b) fraction of the points are noisy samples from a low-dimensional subspace while \u000b fraction of the points can be arbitrary outliers, the goal is to recover the subspace accurately. Existing results for OR-PCA have serious drawbacks: while some results are quite weak in the presence of noise, other results have runtime quadratic in dimension, rendering them impractical for large scale applications.<\/p>\n
In this work, we provide a novel thresholding based iterative algorithm with per-iteration complexity at most linear in the data size. Moreover, the fraction of outliers, \u000b, that our method can handle is tight up to constants while providing nearly optimal computational complexity for a general noise setting. For the special case where the inliers are obtained from a low-dimensional subspace with additive Gaussian noise, we show that a modification of our thresholding based method leads to significant improvement in recovery error (of the subspace) even in the presence of a large fraction of outliers.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix M\u0003, where (1 – cx\u000b) fraction of the points are noisy samples from a low-dimensional subspace while \u000b fraction of the points can be arbitrary 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