Confusion matrix

Confusion Matrix

A confusion matrix is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one. It is a tool often used in the field of machine learning and statistics to evaluate the accuracy of a classification model.

Structure of a Confusion Matrix

A confusion matrix is a square matrix that compares the actual target values with those predicted by the model. It is composed of four key components:

Actual \ Predicted	Positive	Negative
Positive	True Positive (TP)	False Negative (FN)
Negative	False Positive (FP)	True Negative (TN)

• True Positive (TP): The number of instances that are correctly predicted as positive.
• False Positive (FP): The number of instances that are incorrectly predicted as positive.
• True Negative (TN): The number of instances that are correctly predicted as negative.
• False Negative (FN): The number of instances that are incorrectly predicted as negative.

Metrics Derived from a Confusion Matrix

Several important metrics can be derived from the confusion matrix, which are crucial for understanding the performance of a classification model:

• Accuracy: The proportion of the total number of predictions that were correct.

 : Accuracy = \( \frac{TP + TN}{TP + FP + TN + FN} \)

• Precision: The proportion of positive identifications that were actually correct.

 : Precision = \( \frac{TP}{TP + FP} \)

• Recall (also known as Sensitivity or True Positive Rate): The proportion of actual positives that were identified correctly.

 : Recall = \( \frac{TP}{TP + FN} \)

• Specificity: The proportion of actual negatives that were identified correctly.

 : Specificity = \( \frac{TN}{TN + FP} \)

• F1 Score: The harmonic mean of precision and recall, providing a balance between the two.

 : F1 Score = \( 2 \times \frac{Precision \times Recall}{Precision + Recall} \)

Applications

Confusion matrices are widely used in various fields such as:

• Healthcare: To evaluate the performance of diagnostic tests.
• Finance: To assess the accuracy of credit scoring models.
• Marketing: To measure the effectiveness of customer segmentation models.

Limitations

While confusion matrices provide a comprehensive overview of a model's performance, they have limitations:

• They do not provide a single measure of performance, which can make comparisons between models difficult.
• They are not useful for imbalanced datasets, where the number of instances in different classes varies significantly.

See Also

• Receiver Operating Characteristic
• Precision and Recall
• Classification Algorithm

References

• ,

 Pattern Recognition and Machine Learning, 
  
 Springer, 
 2006, 
  
  
 ISBN 978-0-387-31073-2,

• ,

 An introduction to ROC analysis, 
 Pattern Recognition Letters, 
 2006,
 Vol. 27(Issue: 8),
 pp. 861–874,
 DOI: 10.1016/j.patrec.2005.10.010,