The following definitions should be used
Mean errorÂ
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M = \frac{1}{MS_w} \sum_{i=1}^n w_i (x_f - x_v)_i |
where the sum of the weights
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MS_w = \sum_{i=1}^n w_i |
Root mean square (rms) error
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rms = \sqrt {\frac{1}{MS_w} \sum_{i=1}^n w_i (x_f - x_v)_i^2 } |
...
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rms = \sqrt {\frac{1}{MS_w} \sum_{i=1}^n w_i (\vec{V}_f - \vec{V}_v)_i^2 } |
...
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MAE = \frac{1}{MS_w} \sum_{i=1}^n w_i | x_f - x_v |_i |
...
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rmsa = \sqrt {\frac{1}{MS_w} \sum_{i=1}^n w_i (x - x_c)_i^2 } |
...
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M_x = \frac{1}{MS_w} \sum_{i=1}^n w_i x_i |
S1 score
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S_1S1 = 100 \frac{\sum_{i=1}^n w_i (e_g)_i}{\sum_{i=1}^n w_i (G_L)_i} |
...
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e_g = \left ( \left | \frac{\partial}{\partial x}(x_f-x_v)\right | + \left | \frac{\partial}{\partial y}(x_f-x_v)\right | \right ) |
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G_L = \max \left ( \left | \frac{\partial x_f}{\partial x}\right | , \left | \frac{\partial x_v}{\partial x}\right | \right) + \max \left ( \left | \frac{\partial x_f}{\partial y}\right | , \left | \frac{\partial x_v}{\partial y}\right | \right) |
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