In Wu, MT. Confusion matrix and minimum cross-entropy metrics based motion recognition system in the classroom. Sci Rep 12, 3095 (2022). https://doi.org/10.1038/s41598-022-07137-z the author uses a peculiar "cross-entropy formula",
$$ L=-\sum_i (TPR_i + FPR_i) + \log (PPV_i + NPV_i) $$
where
- TPR is the sensitivity. $TP/(TP+FN)$
- FPR is a False Positive Rate, $FP/(FP+TN)$
- PPV is Positive Predictive Value, $TP/(TP+FP)$
- NPV is Negative Predictive Value, $TN/(FN+TN)$
Can you explain how this idea is related to usual cross-entropy? It seems that its main usage is to optimise for the cut point that defines a positive value.
