Plotting ROC Curve with Multiple Classes

问题

I am following the documentation for plotting ROC curves for multiple classes at this link: http://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html

I am confused about this line in particular:

y_score = classifier.fit(X_train, y_train).decision_function(X_test)

I've seen that in other examples, y_score holds probabilities, and they are all positive values, as we would expect. However, the y_score (each column for classes A-C) in this example has mostly negative values. Interestingly, they still add up to -1:

In: y_score[0:5,:]
Out: array([[-0.76305896, -0.36472635,  0.1239796 ],
            [-0.20238399, -0.63148982, -0.16616656],
            [ 0.11808492, -0.80262259, -0.32062486],
            [-0.90750303, -0.1239792 ,  0.02184016],
            [-0.01108555, -0.27918155, -0.71882525]])

How am I supposed to interpret this? And how can I tell just from the y_score which class is the model's prediction for each input?

Edit: all the relevant code:

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

from sklearn import svm, datasets
from sklearn.metrics import roc_curve, auc
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import label_binarize
from sklearn.multiclass import OneVsRestClassifier
from scipy import interp

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

# Binarize the output
y = label_binarize(y, classes=[0, 1, 2])
n_classes = y.shape[1]

# Add noisy features to make the problem harder
random_state = np.random.RandomState(0)
n_samples, n_features = X.shape
X = np.c_[X, random_state.randn(n_samples, 200 * n_features)]

# shuffle and split training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.5,
                                                    random_state=0)

# Learn to predict each class against the other
classifier = OneVsRestClassifier(svm.SVC(kernel='linear', 
                                 probability=True,
                                 random_state=random_state))
y_score = classifier.fit(X_train, y_train).decision_function(X_test)

回答1:

The decision_function returns the distance of the sample from the decision boundary of each class. It wouldn't be the probability. If you want to find out probability, you would use the predict_proba method. If you want to find out what class the estimator assigns the sample, then use predict.

from sklearn import svm, datasets
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import label_binarize
from sklearn.multiclass import OneVsRestClassifier

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

# Binarize the output
y = label_binarize(y, classes=[0, 1, 2])
n_classes = y.shape[1]

# Add noisy features to make the problem harder
random_state = np.random.RandomState(0)
n_samples, n_features = X.shape
X = np.c_[X, random_state.randn(n_samples, 200 * n_features)]

# shuffle and split training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.5,
                                                    random_state=0)

# Learn to predict each class against the other
classifier = OneVsRestClassifier(svm.SVC(kernel='linear', 
                                 probability=True,
                                 random_state=random_state))

# train the classifier
classifer.fit(X_train, y_train)

# generate y_score
y_score = classifier.decision_function(X_test)

# generate probabilities
y_prob = classifier.predict_proba(X_test)

# generate predictions
y_pred = classifier.predict(X_test)

Result:

>>> y_score[0:5,:]
array([[-0.76305896, -0.36472635,  0.1239796 ],
       [-0.20238399, -0.63148982, -0.16616656],
       [ 0.11808492, -0.80262259, -0.32062486],
       [-0.90750303, -0.1239792 ,  0.02184016],
       [-0.01108555, -0.27918155, -0.71882525]])
>>> y_prob[0:5,:]
array([[0.06019732, 0.24174159, 0.8293423 ],
       [0.35610687, 0.30121076, 0.46392587],
       [0.65735935, 0.34605074, 0.25675446],
       [0.03458982, 0.19539083, 0.72575167],
       [0.53656981, 0.22445759, 0.03221816]])
>>> y_pred[0:5,:]
array([[0, 0, 1],
       [0, 0, 0],
       [1, 0, 0],
       [0, 0, 1],
       [0, 0, 0]])

回答2:

To actually plot the multi-class ROC use label_binarize function.

Example using Iris data:

import matplotlib.pyplot as plt
from sklearn import svm, datasets
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import label_binarize
from sklearn.metrics import roc_curve, auc
from sklearn.multiclass import OneVsRestClassifier

iris = datasets.load_iris()
X = iris.data
y = iris.target

# Binarize the output
y = label_binarize(y, classes=[0, 1, 2])
n_classes = y.shape[1]

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.5, random_state=0)

classifier = OneVsRestClassifier(svm.SVC(kernel='linear', probability=True,
                                 random_state=0))
y_score = classifier.fit(X_train, y_train).decision_function(X_test)

fpr = dict()
tpr = dict()
roc_auc = dict()
for i in range(n_classes):
    fpr[i], tpr[i], _ = roc_curve(y_test[:, i], y_score[:, i])
    roc_auc[i] = auc(fpr[i], tpr[i])
colors = cycle(['blue', 'red', 'green'])
for i, color in zip(range(n_classes), colors):
    plt.plot(fpr[i], tpr[i], color=color, lw=lw,
             label='ROC curve of class {0} (area = {1:0.2f})'
             ''.format(i, roc_auc[i]))
plt.plot([0, 1], [0, 1], 'k--', lw=lw)
plt.xlim([-0.05, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver operating characteristic for multi-class data')
plt.legend(loc="lower right")
plt.show()

来源：https://stackoverflow.com/questions/50941223/plotting-roc-curve-with-multiple-classes