Confusion Matrix

A confusion matrix, typically represented as a table, is a popular evaluation metric used to describe the performance of a classification model (or "classifier"). The table compares predicted and actual values. The basic components of the table are as follows:

  • True positives (TP): The prediction was yes, and the true value is yes

  • True negatives (TN): The prediction was no, and the true value is no

  • False positives (FP): The prediction was yes, but the true value was no

  • False negatives (FN): The prediction was no, but the the true value is yes

The confusion matrix is closely related to other metrics like Precision, Recall/Sensitivity, Specificity, and F1 Score. Those definitions are as follows:

Metric

Formula

Definition

Accuracy

(TP+TN)/(TP+TN+FP+FN)

Percentage of total items classified correctly

Precision

TP/(TP+FP)

How accurate the positive predictions are

Recall/Sensitivity

TP/(TP+FN)

True positive rate (eg to asses false positive rate)

Specificity

TN/(TN+FP)

True negative rate (eg to assess false negative rate)

F1 score

2TP/(2TP+FP+FN)

A weighted average of precision and recall