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What is a confusion matrix?

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The confusion matrix is a 2X2 table that contains 4 outputs provided by the binary classifier. Various measures, such as error-rate, accuracy, specificity, sensitivity, precision and recall are derived from it. Confusion Matrix


A data set used for performance evaluation is called a test data set. It should contain the correct labels and predicted labels.


The predicted labels will exactly the same if the performance of a binary classifier is perfect.


The predicted labels usually match with part of the observed labels in real-world scenarios.


A binary classifier predicts all data instances of a test data set as either positive or negative. This produces four outcomes-

1. True-positive(TP) — Correct positive prediction

2. False-positive(FP) — Incorrect positive prediction

3. True-negative(TN) — Correct negative prediction

4. False-negative(FN) — Incorrect negative prediction


Basic measures derived from the confusion matrix

1. Error Rate = (FP+FN)/(P+N)

2. Accuracy = (TP+TN)/(P+N)

3. Sensitivity(Recall or True positive rate) = TP/P

4. Specificity(True negative rate) = TN/N

5. Precision(Positive predicted value) = TP/(TP+FP)

6. F-Score(Harmonic mean of precision and recall) = (1+b)(PREC.REC)/(b²PREC+REC) where b is commonly 0.5, 1, 2.

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