Research Article
A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation
Table 5
The algorithm’s background separation experiment number index of SBMnet.
| Algorithms | Evaluation indexes | AB | BS | CP | GC | HH | To |
| GoDec [38] | RE | 3.6720e − 05 | 3.6753e − 05 | 7.6534e − 04 | 9.6543e − 05 | 0.5632e − 04 | 0.5634e − 03 | Iteration | 38 | 86 | 62 | 18 | 99 | 6 | Rank () | 57 | 68 | 52 | 26 | 89 | 4 | RMSE | 0.6621 | 0.5793 | 0.6735 | 0.6756 | 0.5987 | 0.7624 | CPU time(s) | 13.5822 | 7.146 | 4.3845 | 2.7945 | 17.9202 | 0.32478 |
| ALM | RE | 3.8976e − 06 | 9.6735e − 06 | 3.7865e − 06 | 3.8732e − 06 | 4.7650e − 06 | 8.6723e − 06 | Iteration | 183 | 267 | 206 | 49 | 667 | 32 | Rank () | 335 | 438 | 310 | 169 | 1080 | 6 | RMSE | 0.6723 | 0.6889 | 0.7623 | 0.6724 | 0.6521 | 0.6617 | CPU time(s) | 2819.9870 | 5816.2657 | 4890.2370 | 872.6000 | 7623.8876 | 520.2010 |
| RegL1-ALM [24] | RE | 6.582e − 06 | 7.4981e − 06 | 4.159e − 06 | 3.4045e − 06 | 7.5781e − 08 | 4.7509e − 07 | Iteration | 36 | 38 | 35 | 31 | 42 | 31 | Rank () | 296 | 321 | 244 | 164 | 953 | 3 | RMSE | 0.7689 | 0.6229 | 0.6281 | 0.5225 | 0.6790 | 0.6623 | CPU time(s) | 240.8317 | 111.1153 | 63.863 | 39.3734 | 458.8552 | 2.4931 |
| NCRPCA | RE | 6.9508e − 10 | 2.0525e − 09 | 2.128e − 09 | 1.5526e − 10 | 7.9364e − 10 | 1.8266e − 11 | Iteration | 33 | 32 | 28 | 26 | 46 | 20 | Rank () | 2 | 5 | 7 | 13 | 22 | 3 | RMSE | 0.6022 | 0.5187 | 0.5965 | 0.5562 | 0.7217 | 0.7893 | CPU time(s) | 30.0727 | 15.4769 | 8.8945 | 5.0345 | 82.1707 | 0.28524 |
| GOSUS [19] | RE | 3.45e − 01 | 1.69e − 01 | 2.32e+00 | 3.05e − 01 | 2.71e − 01 | NaN | Iteration | 12 | 16 | 15 | 10 | 16 | NaN | Rank () | 237 | 308 | 209 | 153 | 389 | NaN | RMSE | 0.6832 | 0.7390 | 0.6899 | 0.7023 | 0.7621 | NaN | CPU time(s) | 18.298 | 6.915 | 4.6814 | 3.7101 | 14.7244 | NaN |
| SLM [22] | RE | 3.8908e − 08 | 7.6754e − 09 | 8.6543e − 08 | 8.3276e − 07 | 8.3326e − 08 | 0.6732e − 07 | Iteration | 37 | 49 | 42 | 36 | 42 | 17 | Rank () | 48 | 59 | 43 | 32 | 69 | 4 | RMSE | 0.5622 | 0.5016 | 0.6523 | 0.5286 | 0.6317 | 0.7701 | CPU time(s) | 23.3612 | 48.3233 | 40.6398 | 42.1232 | 46.2219 | 3.2134 |
| NNCRPCA | RE | 5.7823e − 10 | 7.6765e − 11 | 3.6745e − 11 | 5.7628e − 12 | 6.3224e − 10 | 9.7862e − 12 | Iteration | 38 | 42 | 28 | 20 | 36 | 13 | Rank () | 2 | 4 | 4 | 8 | 18 | 3 | RMSE | 0.5521 | 0.5032 | 0.5066 | 0.5489 | 0.6213 | 0.7230 | CPU time(s) | 28.3789 | 56.2231 | 47.3897 | 49.2238 | 52.5487 | 6.1020 |
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AB: Advertisement Board; BS: Bus Station; CP: Camera Parameter; GC: Group Campus; HH: highway; To: Toscana.
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