When I evaluted my model, I always get equal values for metrics : accuracy, precision, recall, and f-measure. Is that possible?
1 Answer
Yes, possible, first of all, everything can be $0$ or $1$, and so equal. In other cases, if precision and recall are equal, then F-measure is equal to them, because it is the harmonic mean of the two. Let's contemplate about how the first three can be equal:
$$\text{Precision}=\frac{TP}{TP+FP}, \ \ \ \text{Recall}=\frac{TP}{TP+FN}, \ \ \text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$$ If $FP=FN$, then precision is equal to recall. Then, $$\frac{TP+TN}{TP+TN+2FP}=\frac{TP}{TP+FP}\rightarrow (TP+TN)\times FP=2TP\times FP$$ So, if $FP=0$, i.e. everything is correct; or, if $FP=FN\neq 0$ and $TN=TP$, all three (consequently all four) are equal.