How to extract False Positive, False Negative from a confusion matrix of multiclass classification

Question

I am classifying mnist data using following Keras code. From confusion_matrix command of sklearn.metrics i got confusion matrix and from True

Answer 1

First of all, you have omissions in your code - in order to run, I needed to add the following commands:

import keras
(x_train, y_train), (x_test, y_test) = mnist.load_data()

Having done that, and given the confusion matrix cm1:

array([[ 965,    0,    1,    0,    0,    2,    6,    1,    5,    0],
       [   0, 1113,    4,    2,    0,    0,    3,    0,   13,    0],
       [   8,    0,  963,   14,    5,    1,    7,    8,   21,    5],
       [   0,    0,    3,  978,    0,    7,    0,    6,   12,    4],
       [   1,    0,    4,    0,  922,    0,    9,    3,    3,   40],
       [   4,    1,    1,   27,    0,  824,    6,    1,   20,    8],
       [  11,    3,    1,    1,    5,    6,  925,    0,    6,    0],
       [   2,    6,   17,    8,    2,    0,    1,  961,    2,   29],
       [   5,    1,    2,   13,    4,    6,    2,    6,  929,    6],
       [   6,    5,    0,    7,    5,    6,    1,    6,   10,  963]])

here is how you can get the requested TP, FP, FN, TN per class:

The True Positives are simply the diagonal elements:

TruePositive = np.diag(cm1)
TruePositive
# array([ 965, 1113,  963,  978,  922,  824,  925,  961,  929,  963])

The False Positives are the sum of the respective column, minus the diagonal element:

FalsePositive = []
for i in range(num_classes):
    FalsePositive.append(sum(cm1[:,i]) - cm1[i,i])
FalsePositive
# [37, 16, 33, 72, 21, 28, 35, 31, 92, 92]

Similarly, the False Negatives are the sum of the respective row, minus the diagonal element:

FalseNegative = []
for i in range(num_classes):
    FalseNegative.append(sum(cm1[i,:]) - cm1[i,i])
FalseNegative
# [15, 22, 69, 32, 60, 68, 33, 67, 45, 46]

Now, the True Negatives are a little trickier; let's first think what exactly a True Negative means, with respect to, say class 0: it means all the samples that have been correctly identified as not being 0. So, essentially what we should do is remove the corresponding row & column from the confusion matrix, and then sum up all the remaining elements:

TrueNegative = []
for i in range(num_classes):
    temp = np.delete(cm1, i, 0)   # delete ith row
    temp = np.delete(temp, i, 1)  # delete ith column
    TrueNegative.append(sum(sum(temp)))
TrueNegative
# [8998, 8871, 9004, 8950, 9057, 9148, 9040, 9008, 8979, 8945]

Let's make a sanity check: for each class, the sum of TP, FP, FN, and TN must be equal to the size of our test set (here 10,000): let's confirm that this is indeed the case:

l = len(y_test)
for i in range(num_classes):
    print(TruePositive[i] + FalsePositive[i] + FalseNegative[i] + TrueNegative[i] == l)

The result is

True
True
True
True
True
True
True
True
True
True