## Introduction

In the realm of machine learning, a confusion matrix is a vital tool for evaluating the performance of classification models. It provides a comprehensive overview of the model’s predictions through four key metrics: True Positive (TP), False Negative (FN), False Positive (FP), and True Negative (TN). This article aims to elucidate the intricacies of a confusion matrix, detailing its components and illustrating how to interpret and calculate various performance metrics.

## What is a Confusion Matrix?

A confusion matrix serves as a quantitative measure of a classification model’s effectiveness. It distills classification results into TP, FN, FP, and TN. Beyond these basic metrics, the confusion matrix facilitates the computation of versatile metrics like accuracy, precision, recall, F1 score, True Positive Rate (TPR), False Negative Rate (FNR), False Positive Rate (FPR), True Negative Rate (TNR), False Discovery Rate (FDR), and Matthews Correlation Coefficient (MCC).

## How to Read a Confusion Matrix

Breaking down a confusion matrix reveals its four components:

• True Positive (TP): Correctly predicted positive instances.
• False Negative (FN): Incorrectly predicted negative instances.
• False Positive (FP): Incorrectly predicted positive instances.
• True Negative (TN): Correctly predicted negative instances.

These components form the basis for calculating performance metrics.

## Calculating Metrics using Confusion Matrix Example

• TP: 80
• FN: 70
• FP: 20
• TN: 30

### Metrics Calculations:

1. Accuracy:
• Formula: accuracy = (TP + TN) / (TP + FN + FP + TN)
• Result: 0.55 (55%)
2. Precision:
• Formula: precision = TP / (TP + FP)
• Result: 0.8 (80%)
3. Recall:
• Formula: recall = TP / (TP + FN)
• Result: 0.53 (53%)
4. F1 Score:
• Formula: F1 score = (2 * precision * recall) / (precision + recall)
• Result: 0.64
5. True Positive Rate (TPR):
• Formula: TPR = TP / (TP + FN)
• Result: 0.53 (53%)
6. False Negative Rate (FNR):
• Formula: FNR = FN / (TP + FN)
• Result: 0.47 (47%)
7. False Positive Rate (FPR):
• Formula: FPR = FP / (FP + TN)
• Result: 0.4 (40%)
8. True Negative Rate (TNR):
• Formula: TNR = TN / (TN + FP)
• Result: 0.6 (60%)
9. False Discovery Rate (FDR):
• Formula: FDR = FP / (TP + FP)
• Result: 0.2 (20%)
10. Matthews Correlation Coefficient (MCC):
• Formula: MCC = (TP * TN – FP * FN) / √((TP + FP) * (TN + FN) * (FP + TN) * (TP + FN))
• Result: 0.11547

## Conclusion

Understanding and interpreting a confusion matrix is crucial for assessing the efficacy of a classification model. The presented example and calculations demonstrate how various metrics can be derived, providing a comprehensive evaluation of the model’s performance. For a hassle-free experience, utilize our Confusion Matrix Calculator.