Understanding Confusion Matrices and Calculating Accuracy in Pandas

Confusion matrices are a fundamental concept in machine learning and statistics. They provide a comprehensive overview of the performance of a classification model by comparing its predicted outcomes with actual labels.

In this article, we will delve into the world of confusion matrices, specifically how to extract accuracy from a pandas-crosstab product using Python’s pandas library without relying on additional libraries like scikit-learn. We will explore various approaches, including utilizing numpy and leveraging pandas’ built-in functionality.

Introduction

A confusion matrix is a square table used to evaluate the performance of a classification model. The table contains four quadrants:

1. True Positives (TP): Correctly predicted positive outcomes.
2. False Positives (FP): Incorrectly predicted positive outcomes.
3. True Negatives (TN): Correctly predicted negative outcomes.
4. False Negatives (FN): Incorrectly predicted negative outcomes.

The formula to calculate accuracy from a confusion matrix is:

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

However, the pandas crosstab function doesn’t provide an easy way to directly calculate this. We need to use numpy and manipulate the resulting array to extract accuracy.

Using Pandas’ Crosstab

The pd.crosstab function in pandas is used to compute a contingency table. It takes two variables as input and returns a dataframe with the counts of each combination.

# Importing necessary libraries
import pandas as pd
import numpy as np

# Creating example dataframes for demonstration purposes
np.random.seed(123)
test_data = pd.DataFrame({'class':np.random.randint(0,2,10),
                        'predicted':np.random.randint(0,2,10)})

tab = pd.crosstab(test_data['class'], test_data['predicted'])

Calculating Accuracy with Numpy

To calculate accuracy from a confusion matrix, we need to use numpy’s diag function to sum the diagonal elements and then divide by the total number of observations.

# Convert the crosstab dataframe to a numpy array
tab_array = tab.to_numpy()

# Use numpy's diag function to get the sum of the diagonal elements
diagonal_sum = np.diag(tab_array)

# Divide by the total number of observations
accuracy = diagonal_sum / tab_array.sum()

Alternatively, you can use np.trace function which returns the trace of an array (sum of elements along its main diagonal).

# Use numpy's trace function to get the sum of the diagonal elements
diagonal_sum = np.trace(tab_array)

# Divide by the total number of observations
accuracy = diagonal_sum / tab_array.sum()

Hardcoding Accuracy

You can also calculate accuracy directly from the crosstab dataframe without using numpy.

# Use hardcoded calculation for demonstration purposes
tab = pd.crosstab(test_data['class'], test_data['predicted'])
accuracy = (tab.iloc[0, 0] + tab.iloc[1, 1]) / tab.to_numpy().sum()

This approach might seem more straightforward but is generally less readable and maintainable than using numpy for calculations.

Discussion

When working with classification models in Python, it’s common to encounter the need to calculate accuracy from a confusion matrix. The pandas crosstab function provides an easy way to create this matrix, but doesn’t offer direct calculation of accuracy.

Using numpy allows us to leverage its powerful array operations and calculations for accuracy extraction. By converting the crosstab dataframe to a numpy array and using np.diag or np.trace functions, we can efficiently calculate the sum of the diagonal elements (TP + TN) and divide by the total number of observations (TP + FP + FN + TN).

While the hardcoded approach might seem simple at first glance, it’s generally recommended to use numpy for calculations involving arrays. This approach promotes code readability and maintainability.

Best Practice

When working with classification models in Python, ensure that you are using pandas’ crosstab function correctly to create confusion matrices. Then, consider using numpy for accurate calculation of accuracy from these matrices. By doing so, you will be able to write efficient and readable code that accurately represents your model’s performance.

Example Code

# Importing necessary libraries
import pandas as pd
import numpy as np

# Creating example dataframes for demonstration purposes
np.random.seed(123)
test_data = pd.DataFrame({'class':np.random.randint(0,2,10),
                        'predicted':np.random.randint(0,2,10)})

tab = pd.crosstab(test_data['class'], test_data['predicted'])

print("Confusion Matrix:")
print(tab)

# Using numpy to calculate accuracy
tab_array = tab.to_numpy()
diagonal_sum = np.diag(tab_array)
accuracy = diagonal_sum / tab_array.sum()

print("\nAccuracy:", accuracy)

# Using hardcoded calculation for demonstration purposes
tab = pd.crosstab(test_data['class'], test_data['predicted'])
accuracy_hardcoded = (tab.iloc[0, 0] + tab.iloc[1, 1]) / tab.to_numpy().sum()

print("\nHardcoded Accuracy:", accuracy_hardcoded)

This example demonstrates the calculation of accuracy from a confusion matrix using both numpy and hardcoded approaches.

Last modified on 2025-01-19