Confusion matrix for Binary classification in Machine Learning

A confusion matrix is a technique for summarizing the performance of a classification algorithm. It is represented in an N x N matrix form where N is the number of target or output classes.

Let’s say we have gender classification problem where input is sample of 12 pictures where 8 are Males and 4 of Females .Lets classify Males belong to class 1(Positive) and Females belong to class 0(Negative) .

The 2X2 confusion matrix would be represented as below.

The table on right represents the same information in terms of true condition.Lets understand the terminologies

TP = A Positive’s prediction is True
FP = A Positive’s prediction is False ( Type I Error )
FN = A Negative’s prediction is True
TN = A Negative’s prediction is False ( Type II Error )

Classification accuracy is measured through different metrics.

• Accuracy

This gives how much we predicted correctly.

Accuracy = correct predictions / total predictions
= ( TP + TN ) / ( TP + FP +TN +FN )

• Precision

Precision = (TP) / (TP+FP)
Measure how many “Positive” predictions are actually correct from all “Positive” predictions .ie when predicted “Positive” how often it is correct .

• Recall

Recall = (TP) / (TP+FN)
It is the measure of correctness of for predictions made for all the “Positive” class .

Classification report through sklearn

# Example of a confusion matrix in Python
from sklearn import metrics

#You need to do actual Predictions to arrive at below values
Actual    = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]
Predicted = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]

cm = metrics.confusion_matrix(Actual, Predicted)
print("============== Confusion Matrix ==================")
print(cm)

print("============ Classification Report ===============")
cr=metrics.classification_report(Actual, Predicted)
print(cr)

print("Precision score: {}".format(metrics.precision_score(Actual,Predicted)))
print("Recall    score: {}".format(metrics.recall_score(Actual,Predicted)))
print("F1        Score: {}".format(metrics.f1_score(Actual,Predicted)))

The output is  below.

References

• https://www.analyticsvidhya.com/blog/2020/04/confusion-matrix-machine-learning/
• https://machinelearningmastery.com/confusion-matrix-machine-learning/
• https://en.wikipedia.org/wiki/Confusion_matrix