Table 2
Performance of interpolation methods and of the proposed ANNs, with and without the removal of outlier from the training set.
| Method | Error factor | Memory | Speed | ||||
|---|---|---|---|---|---|---|---|
| mean | 99th per. | max | (MB) | ms) | |||
| No outlier removal | near. neighbor | ×13.1 | ×11.3 | ×3e5 | 1650 | 62 | |
| linear | 15.7 | ×2.3 | ×143 | 1650 | 1.5e3 | ||
| spline | linear | 15.7 | ×2.3 | ×144 | 1650 | … | |
| cubic | 11.2 | ×2.2 | ×122 | 1650 | … | ||
| quintic | 19.1 | ×2.9 | ×304 | 1650 | … | ||
| RBF | linear | 10.2 | 96.8 | ×99 | 1650 | 1.1e4 | |
| cubic | 10.4 | ×2.1 | ×112 | 1650 | 1.1e4 | ||
| quintic | 10.9 | ×2.1 | ×118 | 1650 | 1.1e4 | ||
| ANN | R | 7.3 | 64.8 | ×81 | 118 | 12 | |
| R+P | 6.2 | 49.7 | ×84 | 118 | 13 | ||
| Outlier removal on training set | near. neighbor | ×13.1 | ×11.6 | ×3e5 | 1650 | 62 | |
| linear | 15.9 | ×2.4 | ×143 | 1650 | 1.5e3 | ||
| spline | linear | 15.9 | ×2.4 | ×144 | 1650 | … | |
| cubic | 11.1 | ×2.2 | ×120 | 1650 | … | ||
| quintic | 20.0 | ×2.7 | ×285 | 1650 | … | ||
| RBF | linear | 10.3 | 97.3 | ×97.5 | 1650 | 1.1e4 | |
| cubic | 10.5 | ×2.0 | ×106 | 1650 | 1.1e4 | ||
| quintic | 10.9 | ×2.0 | ×114 | 1650 | 1.1e4 | ||
| ANN | R | 5.1 | 42.0 | ×32.8 | 118 | 12 | |
| R+P | 5.5 | 42.3 | ×41 | 118 | 13 | ||
| R+P+C | 4.9 | 44.5 | ×44 | 51 | 14 | ||
| R+P+D | 4.5 | 33.1 | ×33.8 | 125 | 11 | ||
| R+P+C+D | 4.8 | 37.9 | ×37.6 | 43 | 14 | ||
Notes. Evaluation speeds are measured on the full set of L lines for 1000 random points. The measurements are performed on a personal laptop equipped with eight logical cores running at 3.00 GHz. Error factors are evaluated on the test set. For neural network architectures, C stands for a line clustering and specialist networks, D for a dense architecture, P for a polynomial transform and R for the design of the last hidden layer using PCA. For each criterion, the best obtained values are highlighted in bold.
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