How to normalize a confusion matrix?

Normalizing a Confusion Matrix

A confusion matrix is a table that summarizes the performance of a classification model. It shows the number of true positives, true negatives, false positives, and false negatives. Normalizing a confusion matrix can help to improve its interpretability and make it easier to compare the performance of different models.

Why Normalize a Confusion Matrix?

• Improved Interpretability: Normalized values make it easier to understand the relative proportions of different classes in the matrix.
• Comparison Across Datasets: Normalization allows comparing the performance of models trained on datasets with different sizes.
• Focus on Proportions: Normalization highlights the proportions of correct and incorrect classifications, rather than the absolute counts.

Methods of Normalization

1. Row-wise Normalization

Each row of the confusion matrix is normalized by dividing each element by the sum of the row.

Code Example

import numpy as np

confusion_matrix = np.array([[10, 2],
                           [3, 8]])

row_normalized_matrix = confusion_matrix / np.sum(confusion_matrix, axis=1, keepdims=True)

print(row_normalized_matrix)

2. Column-wise Normalization

Each column of the confusion matrix is normalized by dividing each element by the sum of the column.

Code Example

import numpy as np

confusion_matrix = np.array([[10, 2],
                           [3, 8]])

column_normalized_matrix = confusion_matrix / np.sum(confusion_matrix, axis=0, keepdims=True)

print(column_normalized_matrix)

3. Global Normalization

The entire confusion matrix is normalized by dividing each element by the total number of samples.

Code Example

import numpy as np

confusion_matrix = np.array([[10, 2],
                           [3, 8]])

global_normalized_matrix = confusion_matrix / np.sum(confusion_matrix)

print(global_normalized_matrix)

Choosing the Right Normalization Method

The choice of normalization method depends on the specific application and the insights you want to obtain from the confusion matrix.

• Row-wise normalization is useful for understanding the predictive performance of the model for each class, independent of the class distribution in the dataset.
• Column-wise normalization is helpful for understanding the model’s ability to correctly classify samples belonging to each class, regardless of the model’s predictions for other classes.
• Global normalization provides an overall measure of the model’s performance, taking into account the distribution of classes in the dataset.

Conclusion

Normalizing a confusion matrix can provide valuable insights into the performance of a classification model and facilitate comparisons across different models or datasets. The choice of normalization method depends on the specific application and the desired insights.