Matthews Correlation Coefficient

A classifier can look successful by repeatedly choosing the common class. Imagine a test set containing 990 legitimate messages and 10 spam messages. Predicting legitimate for every message gives 99% accuracy, yet the filter catches no spam. This is a constructed example of class imbalance, not a reported performance result. MCC helps assess the relationship between predictions and outcomes using correct and incorrect classifications from both classes. In a binary confusion matrix, true positives and true negatives are correct decisions; false positives and false negatives are the two kinds of mistake. A score near positive one indicates strong agreement. Zero indicates no correlation, and negative values indicate an inverse relationship. With both binary classes present, a perfect reversal gives negative one. Consider a different hypothetical classifier with 40 true positives, 40 true negatives and 10 of each kind of error. Its accuracy is 80%, and its MCC is 0.6. Those values describe the same predictions using different scales. An MCC of 0.6 does not mean that 60% of cases were classified correctly. MCC does not decide how costly an error is. A missed machine defect and an unnecessary inspection may have very different consequences. Report the confusion matrix and relevant class-specific metrics alongside MCC, then choose an operating threshold using validation data and the actual decision costs. Scikit-learn provides matthews_corrcoef for binary and multiclass labels. The metric works on predicted classes, so it does not assess whether a claimed 90% probability is trustworthy. Degenerate cases, such as predicting only one class, also need care: the binary formula has a zero denominator, and a library's numeric convention should not be mistaken for a successful classifier.