[科研] | 101级别解释 | Confusion matrix, Accuracy, Precision, Recall and F1 score

Interpretation of Performance Measures

• Different assessment metrics of a classification algorithm for analysing purpose:
  • Confusion Matrix
  • Precision
  • Recall
  • Accuracy
  • Area under ROC curve(AUC)

1. Confusion Matrix

• A table that summarises how successful the classification model is at predicting examples belonging to various classes.
  • One axis is the label that the model predicted,
  • The other axis is the actual label.
• An example:
  

2. Precision

• Precision is a metric that quantifies the number of correct positive predictions made.
• Precision for binary classification:
  $$precision=\frac{TP}{TP+FP}$$

3. Recall

• Recall is a metric that quantifies the number of correct positive predictions made out of all positive predictions that could have been made (which means that recall provides an indication of missed positive predictions).
• Recall for binary classification:
  $$recall=\frac{TP}{TP+FN}$$

4. Accuracy

• Accuracy is a metric that quantifies how close a measurement is to the true or accepted value (which means accuracy takes into account correctly predicted negative predictions).
  $$accuracy=\frac{TP+TN}{TP+FP+TN+FN}$$

5. Area under the ROC curve(AUC)

• It can only be used to assess classifiers that return some confidence score (or a probability) of prediction. For example, logistic regression, neural networks and decision trees (and ensemble models based on decision trees) can be assessed using ROC curves.
• ROC curve commonly use the combination of true positive rate(TPR) and false positive rate(FPR) and that is given as:
  $$TPR=\frac{TP}{TP+FN}$$
  $$FPR=\frac{FP}{FP+TN}$$
• The higher the area under the ROC curve(AUC), the better the classifier.
• An example of the area and ROC curves.
  

F1 score

• F1 score is a weighted average of precision and recall.
  $$F1score=\frac{2}{\frac{1}{precision}+\frac{1}{recall}}=\frac{2\times precision\times recall}{precision+recall}$$

References:

• Confusion matrix, precision, recall and F1 score.
• Recall and precision.
• Accuracy.
• F1 score.