Table 6 Comparison between the number and percentage of outliers outside the 3-sigma limits for the original and hybrid models for 45 high-ranking variables
From: Detecting heterogeneity parameters and hybrid models for precision farming
ML models | Robust method | \(\mu \pm 3\sigma\)(%) | Remarks | |
|---|---|---|---|---|
Before heterogeneity | After heterogeneity | |||
Ridge (control) | Original | 23(1.20) | 29(1.52) | Increase |
M Bi-Square | 25(1.31) | 22(1.15) | Decrease | |
M Hampel | 16(0.84) | 24(1.25) | Increase | |
M Huber | 35(1.83) | 28(1.46) | Decrease | |
MM | 63(3.29) | 22(1.15) | Decrease | |
S | 33(1.72) | 32(1.67) | Decrease | |
Random forest | Original | 45(2.35) | 41(2.14) | Decrease |
M Bi-Square | 26(1.36) | 34(1.78) | Increase | |
M Hampel | 19(0.99) | 29(1.52) | Increase | |
M Huber | 25(1.31) | 33(1.72) | Increase | |
MM | 85(4.44) | 48(2.51) | Decrease | |
S | 75(3.92) | 30(1.57) | Decrease | |
Support vector machine | Original | 24(1.25) | 24(1.25) | Constant |
M Bi-Square | 27(1.41) | 27(1.41) | Constant | |
M Hampel | 23(1.20) | 28(1.46) | Increase | |
M Huber | 27(1.41) | 28(1.46) | Increase | |
MM | 80(4.18) | 68(3.55) | Decrease | |
S | 82(4.28) | 36(1.88) | Decrease | |
Bagging | Original | 31(1.62) | 28(1.56) | Decrease |
M Bi-Square | 34(1.78) | 28(1.46) | Decrease | |
M Hampel | 28(1.46) | 21(1.10) | Decrease | |
M Huber | 30(1.57) | 26(1.36) | Decrease | |
MM | 79(4.13) | 31(1.62) | Decrease | |
S | 75(3.92) | 29(1.52) | Decrease | |
Boosting | Original | 15(0.78) | 14(0.73) | Decrease |
M Bi-Square | 33(1.72) | 25(1.31) | Decrease | |
M Hampel | 29(1.52) | 19(0.99) | Decrease | |
M Huber | 31(1.62) | 25(1.31) | Decrease | |
MM | 94(4.91) | 26(1.36) | Decrease | |
S | 81(4.23) | 31(1.62) | Decrease | |
LASSO | Original | 26(1.36) | 35(1.83) | Increase |
M Bi-Square | 37(1.93) | 42(2.19) | Increase | |
M Hampel | 38(1.99) | 27(1.41) | Decrease | |
M Huber | 41(2.14) | 33(1.72) | Decrease | |
MM | 73(3.81) | 43(2.25) | Decrease | |
S | 54(2.82) | 33(1.72) | Decrease | |
Elastic Net | Original | 29(1.52) | 33(1.72) | Increase |
M Bi-Square | 36(1.88) | 28(1.46) | Decrease | |
M Hampel | 33(1.72) | 23(1.20) | Decrease | |
M Huber | 33(1.72) | 26(1.36) | Decrease | |
MM | 74(3.87) | 30(2.25) | Decrease | |
S | 51(2.67) | 26(1.36) | Decrease | |