Confusion Matrix

Confusion Matrix

Confusion Matrix is a performance measurement tool used in machine learning, particularly for classification problems. It provides a summary of prediction results on a classification problem by comparing the actual labels with those predicted by the model.

What is a Confusion Matrix?

A confusion matrix is a table that describes the performance of a classification model. It shows how many instances were correctly or incorrectly predicted.

Structure of a Confusion Matrix

For a binary classification problem, the confusion matrix looks like this:

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

Terminology

• True Positive (TP): Correctly predicted positives (e.g., predicting a patient has a disease and they actually do)
• False Positive (FP): Incorrectly predicted positives (Type I Error)
• True Negative (TN): Correctly predicted negatives
• False Negative (FN): Incorrectly predicted negatives (Type II Error)

Simple Example

Let’s say a model is predicting if emails are spam:

• TP: Spam email correctly predicted as spam.
• FP: Normal email wrongly predicted as spam.
• TN: Normal email correctly predicted as not spam.
• FN: Spam email wrongly predicted as not spam.

Mathematical Metrics Using the Confusion Matrix

Using TP, TN, FP, and FN, we can calculate several key metrics:

Accuracy

$\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$

Precision

$\text{Precision}=\frac{TP}{TP+FP}$

Recall (Sensitivity)

$\text{Recall}=\frac{TP}{TP+FN}$

F1 Score

$F1=2\cdot \frac{\text{Precision}\cdot \text{Recall}}{\text{Precision}+\text{Recall}}$

Why Use a Confusion Matrix?

• It gives a complete picture of how a model is performing.
• It helps in understanding the types of errors made by the classifier.
• Better than just relying on accuracy, especially when dealing with imbalanced datasets.

Visualization

You can visualize a confusion matrix as a heatmap to easily see where the model is performing well or poorly.

Applications

• Medical diagnosis (e.g., predicting cancer)
• Fraud detection
• Spam detection
• Sentiment analysis

SEO Keywords

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Related Pages

• Precision and Recall
• F1 Score
• Classification
• Model Evaluation Metrics