Confusion matrices

A confusion matrix tabulates predictions against the truth. For binary problems it has four cells:

• True positive (TP): predicted positive, actually positive.
• False positive (FP): predicted positive, actually negative — a false alarm (type I error).
• True negative (TN): predicted negative, actually negative.
• False negative (FN): predicted negative, actually positive — a miss (type II error).

Every common classification metric — accuracy, precision, recall, specificity, F1 — is a ratio of these four counts. For $K$ classes the matrix is $K\times K$; the diagonal holds correct predictions and off-diagonal cells show which classes get confused with which.