Confusion Matrix

A confusion matrix, also called an error matrix, is an evaluation tool often presented as a table of 4 boxes containing 4 essential values to statistically measure/evaluate a result. Generally, from a classification model and/or an artificial intelligence algorithm.

The 4 values are:

— the number of true positives (TP): the number of observations correctly predicted as positive.

— the number of false positives (FP): the number of actual negative observations incorrectly predicted as positive.

— the number of true negatives (TN): the number of observations correctly predicted as negative.

— the number of false negatives (FN): the number of actual positive observations incorrectly predicted as negative.

The 4 values of the confusion matrix make it possible to calculate many other values of statistical interest:

— the rate of true TPR positives, also called sensitivity or recall, TPR = TP / (TP + FN)

— the rate of true FPR negatives, also called specificity, FPR = TN / (FP + TN)

— the positive predictive value, also called precision, PPV = TP / (TP + FP)

— the negative predictive value, NPV = TN / (TN + FN)

— the rate of false positives, FPR = FP / (FP + TN)

— the rate of false negatives, FNR = FN / (FN + TP)

— the rate of false discoveries, FDR = FP / (FP + TP)

— the rate of false omissions, FOR = FN / (FN + TN)

In addition, additional indicators can be useful such as accuracy or F1 score.

By providing a detailed view of classification errors, the Confusion Matrix helps to understand the strengths and weaknesses of the model, thus strengthening the interpretability of the results.