Table III.
EVALUATION METRICS FOR ENSEMBLE METHOD PERMUTATIONS INCLUDING NUMBER OF BASE LEARNERS (TOP PART), COMPARTMENTALIZED VS. NON-COMPARTMENTALIZED BASE LEARNERS (MIDDLE PART), AND BASE LEARNERS OF VARYING ARCHITECTURES (BOTTOM PART)
| Metric | Model | Aorta | Cerebral | Cardiac | Average | |
|---|---|---|---|---|---|---|
| Number of base learners | RE ↓ | Bagging-4 | 9.89% | 28.19% | 29.65% | 22.57% |
| Bagging-8 | 9.71% | 27.67% | 29.20% | 22.19% | ||
| Bagging-12 | 9.69% | 27.22% | 29.13% | 22.01% | ||
| Stacking-4 | 10.22% | 23.97% | 32.24% | 22.14% | ||
| Stacking-8 | 10.81% | 25.18% | 33.11% | 23.03% | ||
| Stacking-12 | 10.77% | 24.90% | 35.81% | 23.83% | ||
| RMSE ↓ | Bagging-4 | (1.46, 0.47, 0.61) | (1.03, 0.86, 0.91) | (2.23, 1.45, 1.99) | (1.57, 0.93, 1.17) | |
| Bagging-8 | (1.41, 0.44, 0.60) | (0.99, 0.85, 0.88) | (2.15, 1.40, 1.86) | (1.52, 0.90, 1.11) | ||
| Bagging-12 | (1.41, 0.44, 0.59) | (0.98, 0.83, 0.88) | (2.13, 1.38, 1.85) | (1.51, 0.88, 1.11) | ||
| Stacking-4 | (1.28, 0.42, 0.48) | (0.80, 0.76, 0.77) | (2.09, 1.56, 1.84) | (1.39, 0.91, 1.03) | ||
| Stacking-8 | (1.39, 0.44, 0.59) | (0.84, 0.78, 0.78) | (2.16, 1.61, 1.97) | (1.46, 0.94, 1.11) | ||
| Stacking-12 | (1.40, 0.52, 0.57) | (0.84, 0.76, 0.75) | (2.10, 1.69, 1.96) | (1.44, 0.99, 1.09) | ||
| k | Bagging-4 | (0.996, 0.972, 0.973) | (0.908, 0.901, 0.897) | (0.890, 0.872, 0.825) | (0.931, 0.915, 0.898) | |
| Bagging-8 | (0.985, 0.968, 0.979) | (0.900, 0.899, 0.899) | (0.882, 0.868, 0.821) | (0.922, 0.912, 0.900) | ||
| Bagging-12 | (0.986, 0.964, 0.979) | (0.899, 0.899, 0.900) | (0.883, 0.867, 0.823) | (0.923, 0.910, 0.901) | ||
| Stacking-4 | (0.974, 0.959, 0.970) | (0.918, 0.899, 0.924) | (0.836, 0.827, 0.775) | (0.909, 0.895, 0.890) | ||
| Stacking-8 | (0.972, 0.958, 0.947) | (0.925, 0.903, 0.906) | (0.827, 0.789, 0.711) | (0.908, 0.883, 0.855) | ||
| Stacking-12 | (0.981, 0.954, 0.969 | (0.937, 0.901, 0.947) | (0.823, 0.768, 0.745) | (0.914, 0.874, 0.887) | ||
| R2 ↑ | Bagging-4 | (0.983, 0.975, 0.981) | (0.891, 0.910, 0.896) | (0.879, 0.884, 0.790) | (0.918, 0.923, 0.889) | |
| Bagging-8 | (0.983, 0.977, 0.981) | (0.897, 0.911, 0.899) | (0.885, 0.893, 0.815) | (0.922, 0.927, 0.898) | ||
| Bagging-12 | (0.983, 0.977, 0.981) | (0.901, 0.915, 0.902) | (0.887, 0.897, 0.817) | (0.924, 0.930, 0.900) | ||
| Stacking-4 | (0.984, 0.981, 0.987) | (0.941, 0.925, 0.921) | (0.881, 0.854, 0.804) | (0.935, 0.920, 0.904) | ||
| Stacking-8 | (0.981, 0.976, 0.982) | (0.934, 0.913, 0.917) | (0.861, 0.837, 0.782) | (0.925, 0.909, 0.894) | ||
| Stacking-12 | (0.980, 0.969, 0.981) | (0.931, 0.919, 0.920) | (0.861, 0.816, 0.780) | (0.924, 0.901, 0.894) | ||
| Metric | Model | Aorta | Cerebral | Cardiac | Average | |
| Compart. vs. Non-compart. | RE ↓ | Bagging Comp-3 | 30.54% | 30.56% | 43.93% | 35.01% |
| Bagging-3 | 9.86% | 27.95% | 29.77% | 22.52% | ||
| Stacking Comp-3 | 11.23% | 24.92% | 35.56% | 23.90% | ||
| Stacking-3 | 9.45% | 24.14% | 31.36% | 21.65% | ||
| RMSE ↓ | Bagging Comp-3 | (11.66, 11.90, 10.28) | (1.26, 1.77, 1.22) | (12.81, 13.38, 11.87) | (8.58, 8.81, 7.79) | |
| Bagging-3 | (1.38, 0.47, 0.62) | (1.01, 0.86, 0.90) | (2.25, 1.46, 1.96) | (1.55, 0.93, 1.16) | ||
| Stacking Comp-3 | (1.41, 0.45, 0.58) | (0.82, 0.72, 0.77) | (2.21, 1.65, 1.95) | (1.48, 0.94, 1.10) | ||
| Stacking-3 | (1.21, 0.39, 0.49) | (0.79, 0.79, 0.77) | (2.11, 1.50, 1.98) | (1.37, 0.89, 1.08) | ||
| k | Bagging Comp-3 | (0.709, 0.638, 0.723) | (0.851, 0.828, 0.836) | (0.825, 0.779, 0.720) | (0.795, 0.748, 0.760) | |
| Bagging-3 | (0.995, 0.965, 0.970) | (0.916, 0.900, 0.894) | (0.897, 0.874, 0.830) | (0.936, 0.913, 0.898) | ||
| Stacking Comp-3 | (0.982, 1.006, 1.005) | (0.923, 0.920, 0.931) | (0.845, 0.825, 0.785) | (0.917, 0.917, 0.907) | ||
| Stacking-3 | (0.971, 0.977, 0.987) | (0.932, 0.902, 0.943) | (0.857, 0.844, 0.770) | (0.920, 0.908, 0.900) | ||
| R2 ↑ | Bagging Comp-3 | (0.954, 0.893, 0.927) | (0.904, 0.905, 0.892) | (0.807, 0.726, 0.679) | (0.888, 0.841, 0.833) | |
| Bagging-3 | (0.984, 0.975, 0.981) | (0.897, 0.911, 0.897) | (0.880, 0.882, 0.799) | (0.920, 0.923, 0.892) | ||
| Stacking Comp-3 | (0.982, 0.976, 0.983) | (0.935, 0.929, 0.918) | (0.864, 0.825, 0.782) | (0.927, 0.910, 0.894) | ||
| Stacking-3 | (0.986, 0.982, 0.987) | (0.940, 0.911, 0.920) | (0.874, 0.865, 0.774) | (0.933, 0.919, 0.894) | ||
| Metric | Model | Aorta | Cerebral | Cardiac | Average | |
| Arch. variation | RE ↓ | Bagging Blocks-3 | 10.35% | 27.94% | 31.28% | 23.19% |
| Stacking Blocks-3 | 9.67% | 23.77% | 31.02% | 21.48% | ||
| RMSE ↓ | Bagging Blocks-3 | (1.39, 0.51, 0.61) | (1.13, 0.93, 0.90) | (2.21, 1.49, 1.92) | (1.58, 0.98, 1.14) | |
| Stacking Blocks-3 | (1.32, 0.38, 0.51) | (0.80, 0.74, 0.76) | (2.00, 1.47, 1.76) | (1.37, 0.86, 1.01) | ||
| k | Bagging Blocks-3 | (0.999, 0.984, 0.977) | (0.956, 0.947, 0.931) | (0.910, 0.883, 0.812) | (0.955, 0.938, 0.907) | |
| Stacking Blocks-3 | (0.980, 1.005, 0.968) | (0.923, 0.909, 0.925) | (0.866, 0.837, 0.814) | (0.923, 0.917, 0.902) | ||
| R2 ↑ | Bagging Blocks-3 | (0.985, 0.977, 0.980) | (0.901, 0.920, 0.903) | (0.881, 0.890, 0.803) | (0.922, 0.929, 0.895) | |
| Stacking Blocks-3 | (0.983, 0.982, 0.986) | (0.936, 0.921, 0.917) | (0.886, 0.874, 0.825) | (0.935, 0.926, 0.909) |
Each metric’s best value is highlighted in bold. Arrows indicate direction of improvement. RMSE given in cm/s. RMSE, and given by .