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What is a Confusion Matrix?

A Confusion matrix is an N x N matrix used for evaluating the performance of a classification model, where N is the number of target classes. The matrix compares the actual target values with those predicted by the machine learning model. This gives us a holistic view of how well our classification model is performing and what kinds of errors it is making.

Confusion Matrix for evaluating the performance of a classification
                            model
  1. The target variable has two values: Positive or Negative
  2. The columns represent the actual values of the target variable
  3. The rows represent the predicted values of the target variable

Understanding True Positive, True Negative, False Positive and False Negative in a Confusion Matrix

  1. True Positive (TP)

    The predicted value matches the actual value. The actual value was positive and the model predicted a positive value

  2. True Negative (TN)

    The predicted value matches the actual value. The actual value was negative and the model predicted a negative value

  3. False Positive (FP) – Type 1 error

    The predicted value was falsely predicted. The actual value was negative but the model predicted a positive value Also known as the Type 1 error

  4. False Negative (FN) – Type 2 error

    The predicted value was falsely predicted. The actual value was positive but the model predicted a negative value Also known as the Type 2 error

Precision vs. Recall

Precision tells us how many of the correctly predicted cases actually turned out to be positive.

Precision Formuls:

              TruePositives / (TruePositives + FalsePositives)

This would determine whether our model is reliable or not.

Recall tells us how many of the actual positive cases we were able to predict correctly with our model.

Recall Formula:

             TruePositives / (TruePositives + FalseNegatives)

Confusion Matrix Recall Formula

F1-score

F1-score is a harmonic mean of Precision and Recall, and so it gives a combined idea about these two metrics. It is maximum when Precision is equal to Recall.

But there is a catch here. The interpretability of the F1-score is poor. This means that we don’t know what our classifier is maximizing – precision or recall? So, we use it in combination with other evaluation metrics which gives us a complete picture of the result.

F1 formula:

            F-Measure = (2 * Precision * Recall) / (Precision + Recall)


Confusion Matrix using scikit-learn in Python

In [2]:
# confusion matrix in sklearn
from sklearn.metrics import confusion_matrix
from sklearn.metrics import classification_report

# actual values
actual = [1,0,0,1,0,0,1,0,0,1]
# predicted values
predicted = [1,0,0,1,0,0,0,1,0,0]

# confusion matrix
matrix = confusion_matrix(actual,predicted, labels=[1,0])
print('Confusion matrix : \n',matrix)

# outcome values order in sklearn
tp, fn, fp, tn = confusion_matrix(actual,predicted,labels=[1,0]).reshape(-1)
print('Outcome values : \n', tp, fn, fp, tn)

# classification report for precision, recall f1-score and accuracy
matrix = classification_report(actual,predicted,labels=[1,0])
print('Classification report : \n',matrix)
Confusion matrix : 
 [[2 2]
 [1 5]]
Outcome values : 
 2 2 1 5
Classification report : 
               precision    recall  f1-score   support

           1       0.67      0.50      0.57         4
           0       0.71      0.83      0.77         6

    accuracy                           0.70        10
   macro avg       0.69      0.67      0.67        10
weighted avg       0.70      0.70      0.69        10

In [ ]: