如何获得一个多类的所有混淆矩阵术语（TPR，FPR，TNR，FNR）？

Question

我有一个代码可以打印多类分类问题的混淆矩阵。在

import itertools
import numpy as np
import matplotlib.pyplot as plt

from sklearn import svm, datasets
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix

# import some data to play with
iris = datasets.load_iris()
X = iris.data
y = iris.target
class_names = iris.target_names

# Split the data into a training set and a test set
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

# Run classifier, using a model that is too regularized (C too low) to see
# the impact on the results
classifier = svm.SVC(kernel='linear', C=0.01)
y_pred = classifier.fit(X_train, y_train).predict(X_test)


def plot_confusion_matrix(cm, classes,
                          normalize=False,
                          title='Confusion matrix',
                          cmap=plt.cm.Blues):
    """
    This function prints and plots the confusion matrix.
    Normalization can be applied by setting `normalize=True`.
    """
    if normalize:
        cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
        print("Normalized confusion matrix")
    else:
        print('Confusion matrix, without normalization')

    print(cm)

    plt.imshow(cm, interpolation='nearest', cmap=cmap)
    plt.title(title)
    plt.colorbar()
    tick_marks = np.arange(len(classes))
    plt.xticks(tick_marks, classes, rotation=45)
    plt.yticks(tick_marks, classes)

    fmt = '.2f' if normalize else 'd'
    thresh = cm.max() / 2.
    for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
        plt.text(j, i, format(cm[i, j], fmt),
                 horizontalalignment="center",
                 color="white" if cm[i, j] > thresh else "black")

    plt.tight_layout()
    plt.ylabel('True label')
    plt.xlabel('Predicted label')

# Compute confusion matrix
cnf_matrix = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision=2)

# Plot non-normalized confusion matrix
plt.figure()
plot_confusion_matrix(cnf_matrix, classes=class_names,
                      title='Confusion matrix, without normalization')

# Plot normalized confusion matrix
plt.figure()
plot_confusion_matrix(cnf_matrix, classes=class_names, normalize=True,
                      title='Normalized confusion matrix')

plt.show()

我想打印其他术语，包括假阳性，真阳性，假阴性，真阴性，假阳性率，假阴性率，为每个班级。在

Answer 1

这是可能的，但你需要编码。使用numpy可以同时对所有类执行此操作：

import numpy as np

print(cnf_matrix)

array([[13,  0,  0],
       [ 0, 10,  6],
       [ 0,  0,  9]])

FP = cnf_matrix.sum(axis=0) - np.diag(cnf_matrix)  
FN = cnf_matrix.sum(axis=1) - np.diag(cnf_matrix)
TP = np.diag(cnf_matrix)
TN = cnf_matrix.sum() - (FP + FN + TP)

FP = FP.astype(float)
FN = FN.astype(float)
TP = TP.astype(float)
TN = TN.astype(float)


# Sensitivity, hit rate, recall, or true positive rate
TPR = TP/(TP+FN)
# Specificity or true negative rate
TNR = TN/(TN+FP) 
# Precision or positive predictive value
PPV = TP/(TP+FP)
# Negative predictive value
NPV = TN/(TN+FN)
# Fall out or false positive rate
FPR = FP/(FP+TN)
# False negative rate
FNR = FN/(TP+FN)
# False discovery rate
FDR = FP/(TP+FP)

# Overall accuracy
ACC = (TP+TN)/(TP+FP+FN+TN)

---

代码背后的思想：这些度量以图形化的方式表示为一个具有许多类的一般情况，如下图所示。在

Answer 2

另一个简单的方法是PyCM，它支持多类混淆矩阵分析。在

示例：

>>> from pycm import ConfusionMatrix
>>> y_true = [1, -1,  0,  0,  1, -1,  1,  0, -1,  0,  1, -1,  1,  0,  0, -1,  0]
>>> y_prediction = [-1, -1,  1,  0,  0,  0,  0, -1,  1, -1,  1,  1,  0,  0,  1,  1, -1]
>>> cm = ConfusionMatrix(actual_vector=y_true,predict_vector=y_prediction)
>>> print(cm)
Predict          -1       0        1        
Actual
-1               1        1        3        
0                3        2        2        
1                1        3        1        




Overall Statistics : 

95% CI                                                           (0.03365,0.43694)
Bennett_S                                                        -0.14706
Chi-Squared                                                      None
Chi-Squared DF                                                   4
Conditional Entropy                                              None
Cramer_V                                                         None
Cross Entropy                                                    1.57986
Gwet_AC1                                                         -0.1436
Joint Entropy                                                    None
KL Divergence                                                    0.01421
Kappa                                                            -0.15104
Kappa 95% CI                                                     (-0.45456,0.15247)
Kappa No Prevalence                                              -0.52941
Kappa Standard Error                                             0.15485
Kappa Unbiased                                                   -0.15405
Lambda A                                                         0.2
Lambda B                                                         0.27273
Mutual Information                                               None
Overall_ACC                                                      0.23529
Overall_RACC                                                     0.33564
Overall_RACCU                                                    0.33737
PPV_Macro                                                        0.23333
PPV_Micro                                                        0.23529
Phi-Squared                                                      None
Reference Entropy                                                1.56565
Response Entropy                                                 1.57986
Scott_PI                                                         -0.15405
Standard Error                                                   0.10288
Strength_Of_Agreement(Altman)                                    Poor
Strength_Of_Agreement(Cicchetti)                                 Poor
Strength_Of_Agreement(Fleiss)                                    Poor
Strength_Of_Agreement(Landis and Koch)                           Poor
TPR_Macro                                                        0.22857
TPR_Micro                                                        0.23529

Class Statistics :

Classes                                                          -1                      0                       1                       
ACC(Accuracy)                                                    0.52941                 0.47059                 0.47059                 
BM(Informedness or bookmaker informedness)                       -0.13333                -0.11429                -0.21667                
DOR(Diagnostic odds ratio)                                       0.5                     0.6                     0.35                    
ERR(Error rate)                                                  0.47059                 0.52941                 0.52941                 
F0.5(F0.5 score)                                                 0.2                     0.32258                 0.17241                 
F1(F1 score - harmonic mean of precision and sensitivity)        0.2                     0.30769                 0.18182                 
F2(F2 score)                                                     0.2                     0.29412                 0.19231                 
FDR(False discovery rate)                                        0.8                     0.66667                 0.83333                 
FN(False negative/miss/type 2 error)                             4                       5                       4                       
FNR(Miss rate or false negative rate)                            0.8                     0.71429                 0.8                     
FOR(False omission rate)                                         0.33333                 0.45455                 0.36364                 
FP(False positive/type 1 error/false alarm)                      4                       4                       5                       
FPR(Fall-out or false positive rate)                             0.33333                 0.4                     0.41667                 
G(G-measure geometric mean of precision and sensitivity)         0.2                     0.30861                 0.18257                 
LR+(Positive likelihood ratio)                                   0.6                     0.71429                 0.48                    
LR-(Negative likelihood ratio)                                   1.2                     1.19048                 1.37143                 
MCC(Matthews correlation coefficient)                            -0.13333                -0.1177                 -0.20658                
MK(Markedness)                                                   -0.13333                -0.12121                -0.19697                
N(Condition negative)                                            12                      10                      12                      
NPV(Negative predictive value)                                   0.66667                 0.54545                 0.63636                 
P(Condition positive)                                            5                       7                       5                       
POP(Population)                                                  17                      17                      17                      
PPV(Precision or positive predictive value)                      0.2                     0.33333                 0.16667                 
PRE(Prevalence)                                                  0.29412                 0.41176                 0.29412                 
RACC(Random accuracy)                                            0.08651                 0.14533                 0.10381                 
RACCU(Random accuracy unbiased)                                  0.08651                 0.14619                 0.10467                 
TN(True negative/correct rejection)                              8                       6                       7                       
TNR(Specificity or true negative rate)                           0.66667                 0.6                     0.58333                 
TON(Test outcome negative)                                       12                      11                      11                      
TOP(Test outcome positive)                                       5                       6                       6                       
TP(True positive/hit)                                            1                       2                       1                       
TPR(Sensitivity, recall, hit rate, or true positive rate)        0.2                     0.28571                 0.2