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fix formula to be seen
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yuweihao authored Apr 29, 2020
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Expand Up @@ -46,7 +46,7 @@ You could also run ./scripts/pretrain_detector.sh to train detector by yourself.
In validation/test dataset, assume there are <img src="https://render.githubusercontent.com/render/math?math=Y" /> images. For each image, a model generates top <img src="https://render.githubusercontent.com/render/math?math=X" /> predicted relationship triplets. As for image <img src="https://render.githubusercontent.com/render/math?math=I_{y}" />, there are <img src="https://render.githubusercontent.com/render/math?math=G_{y}" /> ground truth relationship triplets, where <img src="https://render.githubusercontent.com/render/math?math=T_{y}^{X}" /> triplets are predicted successfully by the model. We can calculate:


<img src="https://render.githubusercontent.com/render/math?math=R"/>@<img src="https://render.githubusercontent.com/render/math?math=X=\frac{1}{Y}\sum_{y=1}^{Y}\frac{T_{y}^{X}}{G_{y}}." />
<img src="https://latex.codecogs.com/gif.latex?R@X=\frac{1}{Y}\sum_{y=1}^{Y}\frac{T_{y}^{X}}{G_{y}}." />


For image <img src="https://render.githubusercontent.com/render/math?math=I_{y}" />, in its <img src="https://render.githubusercontent.com/render/math?math=G_{y}" /> ground truth relationship triplets, there are <img src="https://render.githubusercontent.com/render/math?math=G_{yk}" /> ground truth triplets with relationship <img src="https://render.githubusercontent.com/render/math?math=k" /> (Except <img src="https://render.githubusercontent.com/render/math?math=k=1" />, meaning no relationship. The number of relationship classes is <img src="https://render.githubusercontent.com/render/math?math=K" />, including no relationship), where <img src="https://render.githubusercontent.com/render/math?math=T_{yk}^X" /> triplets are predicted successfully by the model. In <img src="https://render.githubusercontent.com/render/math?math=Y" /> images of validation/test dataset, for relationship <img src="https://render.githubusercontent.com/render/math?math=k" />, there are <img src="https://render.githubusercontent.com/render/math?math=Y_{k}" /> images which contain at least one ground truth triplet with this relationship. The R@X of relationship <img src="https://render.githubusercontent.com/render/math?math=k" /> can be calculated:
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