How to normalize a confusion matrix?

Suppose that

>>> y_true = [0, 0, 1, 1, 2, 0, 1]>>> y_pred = [0, 1, 0, 1, 2, 2, 1]>>> C = confusion_matrix(y_true, y_pred)>>> Carray([[1, 1, 1],       [1, 2, 0],       [0, 0, 1]])

Then, to find out how many samples per class have received their correct label, you need

>>> C / C.astype(np.float).sum(axis=1)array([[ 0.33333333,  0.33333333,  1.        ],       [ 0.33333333,  0.66666667,  0.        ],       [ 0.        ,  0.        ,  1.        ]])

The diagonal contains the required values. Another way to compute these is to realize that what you're computing is the recall per class:

>>> from sklearn.metrics import precision_recall_fscore_support>>> _, recall, _, _ = precision_recall_fscore_support(y_true, y_pred)>>> recallarray([ 0.33333333,  0.66666667,  1.        ])

Similarly, if you divide by the sum over axis=0, you get the precision (fraction of class-k predictions that have ground truth label k):

>>> C / C.astype(np.float).sum(axis=0)array([[ 0.5       ,  0.33333333,  0.5       ],       [ 0.5       ,  0.66666667,  0.        ],       [ 0.        ,  0.        ,  0.5       ]])>>> prec, _, _, _ = precision_recall_fscore_support(y_true, y_pred)>>> precarray([ 0.5       ,  0.66666667,  0.5       ])

From the sklearn documentation (plot example)

cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]

where cm is the confusion matrix as provided by sklearn.

Using Seaborn you can easily print a normalised AND pretty confusion matrix with a heathmap:

from sklearn.metrics import confusion_matriximport seaborn as snscm = confusion_matrix(y_test, y_pred)# Normalisecmn = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]fig, ax = plt.subplots(figsize=(10,10))sns.heatmap(cmn, annot=True, fmt='.2f', xticklabels=target_names, yticklabels=target_names)plt.ylabel('Actual')plt.xlabel('Predicted')plt.show(block=False)