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. Author manuscript; available in PMC: 2011 May 4.
Published in final edited form as: J Mach Learn Res. 2010 Mar 1;11:2287–2322.

Figure 1.

Figure 1

L1: solution for Soft-Impute; L1-U: Post processing after Soft-Impute; L1-L0 Hard-Impute applied to L1-U; C : SVT algorithm; M: OptSpace algorithm. Both Soft-Impute and Pp-SI perform well (prediction error) in the presence of noise. The latter estimates the actual rank of the matrix. Both the Pp-SI and Hard-Impute perform better than Soft-Impute in training error for the same rank or nuclear norm. Hard-Impute and OptSpace perform poorly in prediction error. SVT algorithm does very poorly in prediction error, confirming our claim that (4) causes overfitting — it recovers a matrix with high nuclear norm and rank > 60 where the true rank is only 10. Values of test error larger than one are not shown in the figure. OptSpace is evaluated for a series of ranks ≤ 30.