
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/model_selection/plot_roc.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_model_selection_plot_roc.py>`
        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:


==================================================
Multiclass Receiver Operating Characteristic (ROC)
==================================================

This example describes the use of the Receiver Operating Characteristic (ROC)
metric to evaluate the quality of multiclass classifiers.

ROC curves typically feature true positive rate (TPR) on the Y axis, and false
positive rate (FPR) on the X axis. This means that the top left corner of the
plot is the "ideal" point - a FPR of zero, and a TPR 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 TPR while minimizing the FPR.

ROC curves are typically used in binary classification, where the TPR and FPR
can be defined unambiguously. In the case of multiclass classification, a notion
of TPR or FPR is obtained only after binarizing the output. This can be done in
2 different ways:

- the One-vs-Rest scheme compares each class against all the others (assumed as
  one);
- the One-vs-One scheme compares every unique pairwise combination of classes.

In this example we explore both schemes and demo the concepts of micro and macro
averaging as different ways of summarizing the information of the multiclass ROC
curves.

.. note::

    See :ref:`sphx_glr_auto_examples_model_selection_plot_roc_crossval.py` for
    an extension of the present example estimating the variance of the ROC
    curves and their respective AUC.

.. GENERATED FROM PYTHON SOURCE LINES 37-45

Load and prepare data
=====================

We import the :ref:`iris_dataset` which contains 3 classes, each one
corresponding to a type of iris plant. One class is linearly separable from
the other 2; the latter are **not** linearly separable from each other.

Here we binarize the output and add noisy features to make the problem harder.

.. GENERATED FROM PYTHON SOURCE LINES 45-67

.. code-block:: default


    import numpy as np

    from sklearn.datasets import load_iris
    from sklearn.model_selection import train_test_split

    iris = load_iris()
    target_names = iris.target_names
    X, y = iris.data, iris.target
    y = iris.target_names[y]

    random_state = np.random.RandomState(0)
    n_samples, n_features = X.shape
    n_classes = len(np.unique(y))
    X = np.concatenate([X, random_state.randn(n_samples, 200 * n_features)], axis=1)
    (
        X_train,
        X_test,
        y_train,
        y_test,
    ) = train_test_split(X, y, test_size=0.5, stratify=y, random_state=0)








.. GENERATED FROM PYTHON SOURCE LINES 68-71

We train a :class:`~sklearn.linear_model.LogisticRegression` model which can
naturally handle multiclass problems, thanks to the use of the multinomial
formulation.

.. GENERATED FROM PYTHON SOURCE LINES 71-77

.. code-block:: default


    from sklearn.linear_model import LogisticRegression

    classifier = LogisticRegression()
    y_score = classifier.fit(X_train, y_train).predict_proba(X_test)








.. GENERATED FROM PYTHON SOURCE LINES 78-97

One-vs-Rest multiclass ROC
==========================

The One-vs-the-Rest (OvR) multiclass strategy, also known as one-vs-all,
consists in computing a ROC curve per each of the `n_classes`. In each step, a
given class is regarded as the positive class and the remaining classes are
regarded as the negative class as a bulk.

.. note:: One should not confuse the OvR strategy used for the **evaluation**
    of multiclass classifiers with the OvR strategy used to **train** a
    multiclass classifier by fitting a set of binary classifiers (for instance
    via the :class:`~sklearn.multiclass.OneVsRestClassifier` meta-estimator).
    The OvR ROC evaluation can be used to scrutinize any kind of classification
    models irrespectively of how they were trained (see :ref:`multiclass`).

In this section we use a :class:`~sklearn.preprocessing.LabelBinarizer` to
binarize the target by one-hot-encoding in a OvR fashion. This means that the
target of shape (`n_samples`,) is mapped to a target of shape (`n_samples`,
`n_classes`).

.. GENERATED FROM PYTHON SOURCE LINES 97-104

.. code-block:: default


    from sklearn.preprocessing import LabelBinarizer

    label_binarizer = LabelBinarizer().fit(y_train)
    y_onehot_test = label_binarizer.transform(y_test)
    y_onehot_test.shape  # (n_samples, n_classes)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    (75, 3)



.. GENERATED FROM PYTHON SOURCE LINES 105-106

We can as well easily check the encoding of a specific class:

.. GENERATED FROM PYTHON SOURCE LINES 106-109

.. code-block:: default


    label_binarizer.transform(["virginica"])





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0, 0, 1]])



.. GENERATED FROM PYTHON SOURCE LINES 110-115

ROC curve showing a specific class
----------------------------------

In the following plot we show the resulting ROC curve when regarding the iris
flowers as either "virginica" (`class_id=2`) or "non-virginica" (the rest).

.. GENERATED FROM PYTHON SOURCE LINES 115-120

.. code-block:: default


    class_of_interest = "virginica"
    class_id = np.flatnonzero(label_binarizer.classes_ == class_of_interest)[0]
    class_id





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    2



.. GENERATED FROM PYTHON SOURCE LINES 121-139

.. code-block:: default

    import matplotlib.pyplot as plt

    from sklearn.metrics import RocCurveDisplay

    RocCurveDisplay.from_predictions(
        y_onehot_test[:, class_id],
        y_score[:, class_id],
        name=f"{class_of_interest} vs the rest",
        color="darkorange",
        plot_chance_level=True,
    )
    plt.axis("square")
    plt.xlabel("False Positive Rate")
    plt.ylabel("True Positive Rate")
    plt.title("One-vs-Rest ROC curves:\nVirginica vs (Setosa & Versicolor)")
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_001.png
   :alt: One-vs-Rest ROC curves: Virginica vs (Setosa & Versicolor)
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 140-151

ROC curve using micro-averaged OvR
----------------------------------

Micro-averaging aggregates the contributions from all the classes (using
:func:`numpy.ravel`) to compute the average metrics as follows:

:math:`TPR=\frac{\sum_{c}TP_c}{\sum_{c}(TP_c + FN_c)}` ;

:math:`FPR=\frac{\sum_{c}FP_c}{\sum_{c}(FP_c + TN_c)}` .

We can briefly demo the effect of :func:`numpy.ravel`:

.. GENERATED FROM PYTHON SOURCE LINES 151-156

.. code-block:: default


    print(f"y_score:\n{y_score[0:2,:]}")
    print()
    print(f"y_score.ravel():\n{y_score[0:2,:].ravel()}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    y_score:
    [[0.38 0.05 0.57]
     [0.07 0.28 0.65]]

    y_score.ravel():
    [0.38 0.05 0.57 0.07 0.28 0.65]




.. GENERATED FROM PYTHON SOURCE LINES 157-160

In a multi-class classification setup with highly imbalanced classes,
micro-averaging is preferable over macro-averaging. In such cases, one can
alternatively use a weighted macro-averaging, not demoed here.

.. GENERATED FROM PYTHON SOURCE LINES 160-175

.. code-block:: default


    RocCurveDisplay.from_predictions(
        y_onehot_test.ravel(),
        y_score.ravel(),
        name="micro-average OvR",
        color="darkorange",
        plot_chance_level=True,
    )
    plt.axis("square")
    plt.xlabel("False Positive Rate")
    plt.ylabel("True Positive Rate")
    plt.title("Micro-averaged One-vs-Rest\nReceiver Operating Characteristic")
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_002.png
   :alt: Micro-averaged One-vs-Rest Receiver Operating Characteristic
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 176-179

In the case where the main interest is not the plot but the ROC-AUC score
itself, we can reproduce the value shown in the plot using
:class:`~sklearn.metrics.roc_auc_score`.

.. GENERATED FROM PYTHON SOURCE LINES 179-191

.. code-block:: default


    from sklearn.metrics import roc_auc_score

    micro_roc_auc_ovr = roc_auc_score(
        y_test,
        y_score,
        multi_class="ovr",
        average="micro",
    )

    print(f"Micro-averaged One-vs-Rest ROC AUC score:\n{micro_roc_auc_ovr:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Micro-averaged One-vs-Rest ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 192-195

This is equivalent to computing the ROC curve with
:class:`~sklearn.metrics.roc_curve` and then the area under the curve with
:class:`~sklearn.metrics.auc` for the raveled true and predicted classes.

.. GENERATED FROM PYTHON SOURCE LINES 195-206

.. code-block:: default


    from sklearn.metrics import auc, roc_curve

    # store the fpr, tpr, and roc_auc for all averaging strategies
    fpr, tpr, roc_auc = dict(), dict(), dict()
    # Compute micro-average ROC curve and ROC area
    fpr["micro"], tpr["micro"], _ = roc_curve(y_onehot_test.ravel(), y_score.ravel())
    roc_auc["micro"] = auc(fpr["micro"], tpr["micro"])

    print(f"Micro-averaged One-vs-Rest ROC AUC score:\n{roc_auc['micro']:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Micro-averaged One-vs-Rest ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 207-218

.. note:: By default, the computation of the ROC curve adds a single point at
    the maximal false positive rate by using linear interpolation and the
    McClish correction [:doi:`Analyzing a portion of the ROC curve Med Decis
    Making. 1989 Jul-Sep; 9(3):190-5.<10.1177/0272989x8900900307>`].

ROC curve using the OvR macro-average
-------------------------------------

Obtaining the macro-average requires computing the metric independently for
each class and then taking the average over them, hence treating all classes
equally a priori. We first aggregate the true/false positive rates per class:

.. GENERATED FROM PYTHON SOURCE LINES 218-240

.. code-block:: default


    for i in range(n_classes):
        fpr[i], tpr[i], _ = roc_curve(y_onehot_test[:, i], y_score[:, i])
        roc_auc[i] = auc(fpr[i], tpr[i])

    fpr_grid = np.linspace(0.0, 1.0, 1000)

    # Interpolate all ROC curves at these points
    mean_tpr = np.zeros_like(fpr_grid)

    for i in range(n_classes):
        mean_tpr += np.interp(fpr_grid, fpr[i], tpr[i])  # linear interpolation

    # Average it and compute AUC
    mean_tpr /= n_classes

    fpr["macro"] = fpr_grid
    tpr["macro"] = mean_tpr
    roc_auc["macro"] = auc(fpr["macro"], tpr["macro"])

    print(f"Macro-averaged One-vs-Rest ROC AUC score:\n{roc_auc['macro']:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Macro-averaged One-vs-Rest ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 241-242

This computation is equivalent to simply calling

.. GENERATED FROM PYTHON SOURCE LINES 242-252

.. code-block:: default


    macro_roc_auc_ovr = roc_auc_score(
        y_test,
        y_score,
        multi_class="ovr",
        average="macro",
    )

    print(f"Macro-averaged One-vs-Rest ROC AUC score:\n{macro_roc_auc_ovr:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Macro-averaged One-vs-Rest ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 253-255

Plot all OvR ROC curves together
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 255-296

.. code-block:: default


    from itertools import cycle

    fig, ax = plt.subplots(figsize=(6, 6))

    plt.plot(
        fpr["micro"],
        tpr["micro"],
        label=f"micro-average ROC curve (AUC = {roc_auc['micro']:.2f})",
        color="deeppink",
        linestyle=":",
        linewidth=4,
    )

    plt.plot(
        fpr["macro"],
        tpr["macro"],
        label=f"macro-average ROC curve (AUC = {roc_auc['macro']:.2f})",
        color="navy",
        linestyle=":",
        linewidth=4,
    )

    colors = cycle(["aqua", "darkorange", "cornflowerblue"])
    for class_id, color in zip(range(n_classes), colors):
        RocCurveDisplay.from_predictions(
            y_onehot_test[:, class_id],
            y_score[:, class_id],
            name=f"ROC curve for {target_names[class_id]}",
            color=color,
            ax=ax,
            plot_chance_level=(class_id == 2),
        )

    plt.axis("square")
    plt.xlabel("False Positive Rate")
    plt.ylabel("True Positive Rate")
    plt.title("Extension of Receiver Operating Characteristic\nto One-vs-Rest multiclass")
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_003.png
   :alt: Extension of Receiver Operating Characteristic to One-vs-Rest multiclass
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 297-318

One-vs-One multiclass ROC
=========================

The One-vs-One (OvO) multiclass strategy consists in fitting one classifier
per class pair. Since it requires to train `n_classes` * (`n_classes` - 1) / 2
classifiers, this method is usually slower than One-vs-Rest due to its
O(`n_classes` ^2) complexity.

In this section, we demonstrate the macro-averaged AUC using the OvO scheme
for the 3 possible combinations in the :ref:`iris_dataset`: "setosa" vs
"versicolor", "versicolor" vs "virginica" and  "virginica" vs "setosa". Notice
that micro-averaging is not defined for the OvO scheme.

ROC curve using the OvO macro-average
-------------------------------------

In the OvO scheme, the first step is to identify all possible unique
combinations of pairs. The computation of scores is done by treating one of
the elements in a given pair as the positive class and the other element as
the negative class, then re-computing the score by inversing the roles and
taking the mean of both scores.

.. GENERATED FROM PYTHON SOURCE LINES 318-324

.. code-block:: default


    from itertools import combinations

    pair_list = list(combinations(np.unique(y), 2))
    print(pair_list)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [('setosa', 'versicolor'), ('setosa', 'virginica'), ('versicolor', 'virginica')]




.. GENERATED FROM PYTHON SOURCE LINES 325-379

.. code-block:: default

    pair_scores = []
    mean_tpr = dict()

    for ix, (label_a, label_b) in enumerate(pair_list):
        a_mask = y_test == label_a
        b_mask = y_test == label_b
        ab_mask = np.logical_or(a_mask, b_mask)

        a_true = a_mask[ab_mask]
        b_true = b_mask[ab_mask]

        idx_a = np.flatnonzero(label_binarizer.classes_ == label_a)[0]
        idx_b = np.flatnonzero(label_binarizer.classes_ == label_b)[0]

        fpr_a, tpr_a, _ = roc_curve(a_true, y_score[ab_mask, idx_a])
        fpr_b, tpr_b, _ = roc_curve(b_true, y_score[ab_mask, idx_b])

        mean_tpr[ix] = np.zeros_like(fpr_grid)
        mean_tpr[ix] += np.interp(fpr_grid, fpr_a, tpr_a)
        mean_tpr[ix] += np.interp(fpr_grid, fpr_b, tpr_b)
        mean_tpr[ix] /= 2
        mean_score = auc(fpr_grid, mean_tpr[ix])
        pair_scores.append(mean_score)

        fig, ax = plt.subplots(figsize=(6, 6))
        plt.plot(
            fpr_grid,
            mean_tpr[ix],
            label=f"Mean {label_a} vs {label_b} (AUC = {mean_score :.2f})",
            linestyle=":",
            linewidth=4,
        )
        RocCurveDisplay.from_predictions(
            a_true,
            y_score[ab_mask, idx_a],
            ax=ax,
            name=f"{label_a} as positive class",
        )
        RocCurveDisplay.from_predictions(
            b_true,
            y_score[ab_mask, idx_b],
            ax=ax,
            name=f"{label_b} as positive class",
            plot_chance_level=True,
        )
        plt.axis("square")
        plt.xlabel("False Positive Rate")
        plt.ylabel("True Positive Rate")
        plt.title(f"{target_names[idx_a]} vs {label_b} ROC curves")
        plt.legend()
        plt.show()

    print(f"Macro-averaged One-vs-One ROC AUC score:\n{np.average(pair_scores):.2f}")




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_004.png
         :alt: setosa vs versicolor ROC curves
         :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_005.png
         :alt: setosa vs virginica ROC curves
         :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_006.png
         :alt: versicolor vs virginica ROC curves
         :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_006.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Macro-averaged One-vs-One ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 380-383

One can also assert that the macro-average we computed "by hand" is equivalent
to the implemented `average="macro"` option of the
:class:`~sklearn.metrics.roc_auc_score` function.

.. GENERATED FROM PYTHON SOURCE LINES 383-393

.. code-block:: default


    macro_roc_auc_ovo = roc_auc_score(
        y_test,
        y_score,
        multi_class="ovo",
        average="macro",
    )

    print(f"Macro-averaged One-vs-One ROC AUC score:\n{macro_roc_auc_ovo:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Macro-averaged One-vs-One ROC AUC score:
    0.77




.. GENERATED FROM PYTHON SOURCE LINES 394-396

Plot all OvO ROC curves together
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 396-425

.. code-block:: default


    ovo_tpr = np.zeros_like(fpr_grid)

    fig, ax = plt.subplots(figsize=(6, 6))
    for ix, (label_a, label_b) in enumerate(pair_list):
        ovo_tpr += mean_tpr[ix]
        plt.plot(
            fpr_grid,
            mean_tpr[ix],
            label=f"Mean {label_a} vs {label_b} (AUC = {pair_scores[ix]:.2f})",
        )

    ovo_tpr /= sum(1 for pair in enumerate(pair_list))

    plt.plot(
        fpr_grid,
        ovo_tpr,
        label=f"One-vs-One macro-average (AUC = {macro_roc_auc_ovo:.2f})",
        linestyle=":",
        linewidth=4,
    )
    plt.plot([0, 1], [0, 1], "k--", label="Chance level (AUC = 0.5)")
    plt.axis("square")
    plt.xlabel("False Positive Rate")
    plt.ylabel("True Positive Rate")
    plt.title("Extension of Receiver Operating Characteristic\nto One-vs-One multiclass")
    plt.legend()
    plt.show()




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_roc_007.png
   :alt: Extension of Receiver Operating Characteristic to One-vs-One multiclass
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_roc_007.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 426-443

We confirm that the classes "versicolor" and "virginica" are not well
identified by a linear classifier. Notice that the "virginica"-vs-the-rest
ROC-AUC score (0.77) is between the OvO ROC-AUC scores for "versicolor" vs
"virginica" (0.64) and "setosa" vs "virginica" (0.90). Indeed, the OvO
strategy gives additional information on the confusion between a pair of
classes, at the expense of computational cost when the number of classes
is large.

The OvO strategy is recommended if the user is mainly interested in correctly
identifying a particular class or subset of classes, whereas evaluating the
global performance of a classifier can still be summarized via a given
averaging strategy.

Micro-averaged OvR ROC is dominated by the more frequent class, since the
counts are pooled. The macro-averaged alternative better reflects the
statistics of the less frequent classes, and then is more appropriate when
performance on all the classes is deemed equally important.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.470 seconds)


.. _sphx_glr_download_auto_examples_model_selection_plot_roc.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.3.X?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_roc.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_roc.py <plot_roc.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_roc.ipynb <plot_roc.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
