Compare MulticlassJaccardIndex, MulticlassAccuracy, MulticlassPrecision, MulticlassRecall

[NguyenDuyDuc1995]

Hi, I have some questions.

preds = [2,1,0,0]
targets = [2,1,0,1]

1. About BinaryJaccardIndex and MulticlassJaccardIndex.

• I calculate MulticlassJaccardIndex by MulticlassJaccardIndex command in torchmetrics
• I calculate binaryJaccardIndex for class0, class1, class2 then average them.
• results are the same, it's very good.
  => So I think it will be the same when I calculate MulticlassAccuracy, but they are not. Why is it?
  it means: result from MulticlassAccuracy is different than average of binaryAccuracy of 3 classes.

2. I see the formula of MulticlassAccuracy and MulticlassPrecision, and MulticlassRecall are different. But when I use the classes from torchmetrics, results from Recall always are the same as Accuracy. Why?

3. With the above preds, and targets, could you tell me how to calculate Multiclass Accuracy by hand to prove they are the same with the formula: \text{Accuracy} = \frac{1}{N}\sum_i^N 1(y_i = \hat{y}_i) (https://torchmetrics.readthedocs.io/en/stable/classification/accuracy.html#multiclassaccuracy)

Thank you so much