如何从多类分类的混淆矩阵中提取假阳性、假阴性

Question

我正在使用以下 Keras 代码对 mnist 数据进行分类。从confusion_matrix 的sklearn.metrics 命令我得到了混淆矩阵，从TruePositive= sum(numpy.diag(cm1)) 命令我能够得到真阳性。但我很困惑如何获得真阴性、假阳性、假阴性。我从here 阅读了解决方案，但用户 cmets 让我感到困惑。请帮助编码以获取参数。

from sklearn.metrics import confusion_matrix
import keras
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers import Dense, Dropout, Flatten
from keras.layers import Conv2D, MaxPooling2D
from keras import backend as K
import numpy as np
(x_train, y_train), (x_test, y_test) = mnist.load_data()
batch_size = 128
num_classes = 10
epochs = 1
img_rows, img_cols = 28, 28
y_test1=y_test

if K.image_data_format() == 'channels_first':
    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)
    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)
    input_shape = (1, img_rows, img_cols)
else:
    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)
    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)
    input_shape = (img_rows, img_cols, 1)

x_train = x_train.astype('float32')
x_test = x_test.astype('float32')
x_train /= 255
x_test /= 255

y_train = keras.utils.to_categorical(y_train, num_classes)
y_test = keras.utils.to_categorical(y_test, num_classes)

model = Sequential()
model.add(Conv2D(32, kernel_size=(3, 3),
                 activation='relu',
                 input_shape=input_shape))
model.add(Conv2D(64, (3, 3), activation='relu'))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))
model.add(Flatten())
#model.add(GlobalAveragePooling2D())
#model.add(GlobalMaxPooling2D())
model.add(Dense(128, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(num_classes, activation='softmax'))

model.compile(loss=keras.losses.binary_crossentropy,
              optimizer=keras.optimizers.Adadelta(),
              metrics=['accuracy'])



model.fit(x_train, y_train,
          batch_size=batch_size,
          epochs=epochs,
          verbose=1,
          validation_data=(x_test, y_test))

pre_cls=model.predict_classes(x_test)

cm1 = confusion_matrix(y_test1,pre_cls)
print('Confusion Matrix : \n', cm1)

TruePositive= sum(np.diag(cm1))

Answer 1

首先，你的代码有遗漏——为了运行，我需要添加以下命令：

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

这样做了，并给出了混淆矩阵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]])

这里是您如何获得请求的 TP、FP、FN、TN 每个班级：

真阳性只是对角线元素：

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

误报是各列的总和，减去对角线元素：

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]

同样，假阴性是相应行的总和，减去对角线元素：

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]

现在，真底片有点棘手；让我们首先考虑一下 True Negative 到底意味着什么，比如类 0：它意味着所有被正确识别为不是0的样本。所以，本质上我们应该做的是从混淆矩阵中移除相应的行和列，然后将所有剩余的元素相加：

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]

让我们做一个健全性检查：对于每个类，TP、FP、FN 和 TN 的总和必须等于我们的测试集的大小（这里是 10,000）：让我们确认一下确实如此：

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

结果是

True
True
True
True
True
True
True
True
True
True