Table 1.
Performance of the Soft-Impute on different problem instances. Effective rank is the rank of the recovered matrix at value of λ for (11). Convergence criterion is taken as “fraction of improvement of objective value” less than 10−4. All implementations are done in MATLAB including the MATLAB implementation of PROPACK on a Intel Xeon Linux 3GHz processor. Timings (in seconds) are to be interpreted keeping the MATLAB implementation in mind.
| (m, n) | |Ω| | true rank | SNR | effective rank | time(s) |
|---|---|---|---|---|---|
| (3 × 104, 104) | 104 | 15 | 1 | (13, 47, 80) | (41.9, 124.7, 305.8) |
| (105, 105) | 104 | 15 | 10 | (5, 14, 32, 62) | (37, 74.5, 199.8, 653) |
| (105, 105) | 105 | 15 | 10 | (18, 80) | (202, 1840) |
| (5 × 105, 5 × 105) | 104 | 15 | 10 | 11 | 628.14 |
| (5 × 105, 5 × 105) | 105 | 15 | 1 | (3, 11, 52) | (341.9, 823.4, 4810.75) |
| (106, 106) | 105 | 15 | 1 | 80 | 8906 |