Greedy bilateral sketch, completion & smoothing

Publication Type:
Conference Proceeding
Journal of Machine Learning Research, 2013, 31 pp. 650 - 658
Issue Date:
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Copyright 2013 by the authors. Recovering a large low-rank matrix from highly corrupted, incomplete or sparse outlier over- whelmed observations is the crux of various in- triguing statistical problems. We explore the power of "greedy bilateral (GreB)" paradigm in reducing both time and sample complexities for solving these problems. GreB models a low- rank variable as a bilateral factorization, and up- dates the left and right factors in a mutually adap- tive and greedy incremental manner. We de- tail how to model and solve low-rank approx- imation, matrix completion and robust PCA in GreB's paradigm. On their MATLAB implemen- tations, approximating a noisy 104 × 104 matrix of rank 500 with SVD accuracy takes 6s; Movie- Lens10M matrix of size 69878 × 10677 can be completed in 10s from 30% of 107 ratings with RMSE 0.86 on the rest 70%; the low-rank back- ground and sparse moving outliers in a 120×160 video of 500 frames are accurately separated in 1s. This brings 30 to 100 times acceleration in solving these popular statistical problems.
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