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= 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:

{| class="wikitable"
|-
! 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 ==

* {{Cite book | last1 = Bishop | first1 = Christopher M. | title = Pattern Recognition and Machine Learning | year = 2006 | publisher = Springer | isbn = 978-0-387-31073-2 }}
* {{Cite journal | last1 = Fawcett | first1 = Tom | title = An introduction to ROC analysis | journal = Pattern Recognition Letters | year = 2006 | volume = 27 | issue = 8 | pages = 861–874 | doi = 10.1016/j.patrec.2005.10.010 }}

[[Category:Machine learning]]
[[Category:Statistical classification]]
[[Category:Evaluation methods]]

Confusion matrix - Revision history

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