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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.

                            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              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              =              0.5              ,              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

                            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              ()
Receiver operating characteristic example

Plot ROC curves for the multiclass problem¶

Compute macro-average ROC curve and ROC area

                                # 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                +=                np                .                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 multiclass"                )                plt                .                legend                (                loc                =                "lower right"                )                plt                .                show                ()
Some extension of Receiver operating characteristic to multiclass

Area under ROC for the multiclass problem¶

The 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.

                                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                )                )              
                One-vs-One ROC AUC scores: 0.698586 (macro), 0.665839 (weighted by prevalence) One-vs-Rest ROC AUC scores: 0.698586 (macro), 0.665839 (weighted by prevalence)

Total running time of the script: ( 0 minutes 0.190 seconds)

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