.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_model_selection_plot_roc.py: ======================================= Receiver Operating Characteristic (ROC) ======================================= Example of Receiver Operating Characteristic (ROC) metric to evaluate classifier output quality. ROC curves typically feature true positive rate on the Y axis, and false positive rate on the X axis. This means that the top left corner of the plot is the "ideal" point - a false positive rate of zero, and a true positive rate of one. This is not very realistic, but it does mean that a larger area under the curve (AUC) is usually better. The "steepness" of ROC curves is also important, since it is ideal to maximize the true positive rate while minimizing the false positive rate. ROC curves are typically used in binary classification to study the output of a classifier. In order to extend ROC curve and ROC area to multi-label classification, it is necessary to binarize the output. One ROC curve can be drawn per label, but one can also draw a ROC curve by considering each element of the label indicator matrix as a binary prediction (micro-averaging). Another evaluation measure for multi-label classification is macro-averaging, which gives equal weight to the classification of each label. .. note:: See also :func:`sklearn.metrics.roc_auc_score`, :ref:`sphx_glr_auto_examples_model_selection_plot_roc_crossval.py` .. code-block:: default print(__doc__) 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 from sklearn.metrics import roc_auc_score # 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) # Compute ROC curve and ROC area for each class 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]) # Compute micro-average ROC curve and ROC area fpr["micro"], tpr["micro"], _ = roc_curve(y_test.ravel(), y_score.ravel()) roc_auc["micro"] = auc(fpr["micro"], tpr["micro"]) Plot of a ROC curve for a specific class .. code-block:: default plt.figure() lw = 2 plt.plot(fpr[2], tpr[2], color='darkorange', lw=lw, label='ROC curve (area = %0.2f)' % roc_auc[2]) plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--') plt.xlim([0.0, 1.0]) plt.ylim([0.0, 1.05]) plt.xlabel('False Positive Rate') plt.ylabel('True Positive Rate') plt.title('Receiver operating characteristic example') plt.legend(loc="lower right") plt.show() .. image:: /auto_examples/model_selection/images/sphx_glr_plot_roc_001.png :class: sphx-glr-single-img Plot ROC curves for the multilabel problem .......................................... Compute macro-average ROC curve and ROC area .. code-block:: default # First aggregate all false positive rates all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)])) # Then interpolate all ROC curves at this points mean_tpr = np.zeros_like(all_fpr) for i in range(n_classes): mean_tpr += interp(all_fpr, fpr[i], tpr[i]) # Finally average it and compute AUC mean_tpr /= n_classes fpr["macro"] = all_fpr tpr["macro"] = mean_tpr roc_auc["macro"] = auc(fpr["macro"], tpr["macro"]) # Plot all ROC curves plt.figure() plt.plot(fpr["micro"], tpr["micro"], label='micro-average ROC curve (area = {0:0.2f})' ''.format(roc_auc["micro"]), color='deeppink', linestyle=':', linewidth=4) plt.plot(fpr["macro"], tpr["macro"], label='macro-average ROC curve (area = {0:0.2f})' ''.format(roc_auc["macro"]), color='navy', linestyle=':', linewidth=4) colors = cycle(['aqua', 'darkorange', 'cornflowerblue']) 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([0.0, 1.0]) plt.ylim([0.0, 1.05]) plt.xlabel('False Positive Rate') plt.ylabel('True Positive Rate') plt.title('Some extension of Receiver operating characteristic to multi-class') plt.legend(loc="lower right") plt.show() .. image:: /auto_examples/model_selection/images/sphx_glr_plot_roc_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /home/circleci/project/examples/model_selection/plot_roc.py:112: DeprecationWarning: scipy.interp is deprecated and will be removed in SciPy 2.0.0, use numpy.interp instead mean_tpr += interp(all_fpr, fpr[i], tpr[i]) Area under ROC for the multiclass problem ......................................... The :func:`sklearn.metrics.roc_auc_score` function can be used for multi-class classification. The multi-class One-vs-One scheme compares every unique pairwise combination of classes. In this section, we calculate the AUC using the OvR and OvO schemes. We report a macro average, and a prevalence-weighted average. .. code-block:: default y_prob = classifier.predict_proba(X_test) macro_roc_auc_ovo = roc_auc_score(y_test, y_prob, multi_class="ovo", average="macro") weighted_roc_auc_ovo = roc_auc_score(y_test, y_prob, multi_class="ovo", average="weighted") macro_roc_auc_ovr = roc_auc_score(y_test, y_prob, multi_class="ovr", average="macro") weighted_roc_auc_ovr = roc_auc_score(y_test, y_prob, multi_class="ovr", average="weighted") print("One-vs-One ROC AUC scores:\n{:.6f} (macro),\n{:.6f} " "(weighted by prevalence)" .format(macro_roc_auc_ovo, weighted_roc_auc_ovo)) print("One-vs-Rest ROC AUC scores:\n{:.6f} (macro),\n{:.6f} " "(weighted by prevalence)" .format(macro_roc_auc_ovr, weighted_roc_auc_ovr)) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none One-vs-One ROC AUC scores: 0.767722 (macro), 0.748802 (weighted by prevalence) One-vs-Rest ROC AUC scores: 0.767722 (macro), 0.748802 (weighted by prevalence) .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.787 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_auto_examples_model_selection_plot_roc.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: https://mybinder.org/badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.22.X?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_roc.ipynb :width: 150 px .. container:: sphx-glr-download :download:`Download Python source code: plot_roc.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_roc.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_