.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/miscellaneous/plot_isotonic_regression.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_miscellaneous_plot_isotonic_regression.py>`
        to download the full example code. or to run this example in your browser via JupyterLite or Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_miscellaneous_plot_isotonic_regression.py:


====================
الانحدار الأيزوتوني
====================

توضيح للانحدار الأيزوتوني على بيانات مُولدة (اتجاه أحادي غير خطي مع ضوضاء متجانسة التباين).

خوارزمية الانحدار الأيزوتوني تجد تقريبًا غير متناقص لدالة مع تقليل متوسط مربع الخطأ على بيانات التدريب. ميزة هذا النموذج غير البارامتري هي أنه لا يفترض أي شكل للدالة المستهدفة بخلاف الأحادية. وللمقارنة، يتم تقديم الانحدار الخطي أيضًا.

يوضح الرسم البياني على الجانب الأيمن دالة التنبؤ بالنموذج التي تنتج عن الاستيفاء الخطي لنقاط العتبة. ونقاط العتبة هي مجموعة فرعية من ملاحظات مدخلات التدريب، ويتم حساب قيمها المستهدفة المطابقة بواسطة التلاؤم الأيزوتوني غير البارامتري.

.. GENERATED FROM PYTHON SOURCE LINES 12-28

.. code-block:: Python

    # المؤلفون: مطوري سكايلرن
    # معرف الترخيص: BSD-3-Clause

    import matplotlib.pyplot as plt
    import numpy as np
    from matplotlib.collections import LineCollection

    from sklearn.isotonic import IsotonicRegression
    from sklearn.linear_model import LinearRegression
    from sklearn.utils import check_random_state

    n = 100
    x = np.arange(n)
    rs = check_random_state(0)
    y = rs.randint(-50, 50, size=(n,)) + 50.0 * np.log1p(np.arange(n))








.. GENERATED FROM PYTHON SOURCE LINES 29-30

تناسب نماذج IsotonicRegression وLinearRegression:

.. GENERATED FROM PYTHON SOURCE LINES 30-37

.. code-block:: Python


    ir = IsotonicRegression(out_of_bounds="clip")
    y_ = ir.fit_transform(x, y)

    lr = LinearRegression()
    lr.fit(x[:, np.newaxis], y)  # x يجب أن تكون ثنائية الأبعاد للانحدار الخطي






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-24 {
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      /* Definition of color scheme for unfitted estimators */
      --sklearn-color-unfitted-level-0: #fff5e6;
      --sklearn-color-unfitted-level-1: #f6e4d2;
      --sklearn-color-unfitted-level-2: #ffe0b3;
      --sklearn-color-unfitted-level-3: chocolate;
      /* Definition of color scheme for fitted estimators */
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      --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));
      --sklearn-color-icon: #696969;

      @media (prefers-color-scheme: dark) {
        /* Redefinition of color scheme for dark theme */
        --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));
        --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));
        --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));
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      border: 1px dashed var(--sklearn-color-line);
      margin: 0 0.4em 0.5em 0.4em;
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         but bootstrap.min.css set `[hidden] { display: none !important; }`
         so we also need the `!important` here to be able to override the
         default hidden behavior on the sphinx rendered scikit-learn.org.
         See: https://github.com/scikit-learn/scikit-learn/issues/21755 */
      display: inline-block !important;
      position: relative;
    }

    #sk-container-id-24 div.sk-text-repr-fallback {
      display: none;
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    div.sk-parallel-item,
    div.sk-serial,
    div.sk-item {
      /* draw centered vertical line to link estimators */
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      background-repeat: no-repeat;
      background-position: center center;
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    #sk-container-id-24 div.sk-parallel-item::after {
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      width: 100%;
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      flex-grow: 1;
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    #sk-container-id-24 div.sk-parallel {
      display: flex;
      align-items: stretch;
      justify-content: center;
      background-color: var(--sklearn-color-background);
      position: relative;
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    #sk-container-id-24 div.sk-parallel-item {
      display: flex;
      flex-direction: column;
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    #sk-container-id-24 div.sk-parallel-item:first-child::after {
      align-self: flex-end;
      width: 50%;
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    #sk-container-id-24 div.sk-parallel-item:last-child::after {
      align-self: flex-start;
      width: 50%;
    }

    #sk-container-id-24 div.sk-parallel-item:only-child::after {
      width: 0;
    }

    /* Serial-specific style estimator block */

    #sk-container-id-24 div.sk-serial {
      display: flex;
      flex-direction: column;
      align-items: center;
      background-color: var(--sklearn-color-background);
      padding-right: 1em;
      padding-left: 1em;
    }


    /* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
    clickable and can be expanded/collapsed.
    - Pipeline and ColumnTransformer use this feature and define the default style
    - Estimators will overwrite some part of the style using the `sk-estimator` class
    */

    /* Pipeline and ColumnTransformer style (default) */

    #sk-container-id-24 div.sk-toggleable {
      /* Default theme specific background. It is overwritten whether we have a
      specific estimator or a Pipeline/ColumnTransformer */
      background-color: var(--sklearn-color-background);
    }

    /* Toggleable label */
    #sk-container-id-24 label.sk-toggleable__label {
      cursor: pointer;
      display: flex;
      width: 100%;
      margin-bottom: 0;
      padding: 0.5em;
      box-sizing: border-box;
      text-align: center;
      align-items: start;
      justify-content: space-between;
      gap: 0.5em;
    }

    #sk-container-id-24 label.sk-toggleable__label .caption {
      font-size: 0.6rem;
      font-weight: lighter;
      color: var(--sklearn-color-text-muted);
    }

    #sk-container-id-24 label.sk-toggleable__label-arrow:before {
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      color: var(--sklearn-color-icon);
    }

    #sk-container-id-24 label.sk-toggleable__label-arrow:hover:before {
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      max-width: 0;
      overflow: hidden;
      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content pre {
      margin: 0.2em;
      border-radius: 0.25em;
      color: var(--sklearn-color-text);
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content.fitted pre {
      /* unfitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-24 input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      max-height: 200px;
      max-width: 100%;
      overflow: auto;
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    #sk-container-id-24 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
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    #sk-container-id-24 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-24 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator-specific style */

    /* Colorize estimator box */
    #sk-container-id-24 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-24 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    #sk-container-id-24 div.sk-label label.sk-toggleable__label,
    #sk-container-id-24 div.sk-label label {
      /* The background is the default theme color */
      color: var(--sklearn-color-text-on-default-background);
    }

    /* On hover, darken the color of the background */
    #sk-container-id-24 div.sk-label:hover label.sk-toggleable__label {
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      background-color: var(--sklearn-color-unfitted-level-2);
    }

    /* Label box, darken color on hover, fitted */
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    /* Estimator label */

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    }

    #sk-container-id-24 div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    #sk-container-id-24 div.sk-estimator {
      font-family: monospace;
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: 0.25em;
      box-sizing: border-box;
      margin-bottom: 0.5em;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    /* on hover */
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      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

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      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Specification for estimator info (e.g. "i" and "?") */

    /* Common style for "i" and "?" */

    .sk-estimator-doc-link,
    a:link.sk-estimator-doc-link,
    a:visited.sk-estimator-doc-link {
      float: right;
      font-size: smaller;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-background);
      border-radius: 1em;
      height: 1em;
      width: 1em;
      text-decoration: none !important;
      margin-left: 0.5em;
      text-align: center;
      /* unfitted */
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
      color: var(--sklearn-color-unfitted-level-1);
    }

    .sk-estimator-doc-link.fitted,
    a:link.sk-estimator-doc-link.fitted,
    a:visited.sk-estimator-doc-link.fitted {
      /* fitted */
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    div.sk-estimator:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover,
    div.sk-label-container:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
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    div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover,
    div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    /* Span, style for the box shown on hovering the info icon */
    .sk-estimator-doc-link span {
      display: none;
      z-index: 9999;
      position: relative;
      font-weight: normal;
      right: .2ex;
      padding: .5ex;
      margin: .5ex;
      width: min-content;
      min-width: 20ex;
      max-width: 50ex;
      color: var(--sklearn-color-text);
      box-shadow: 2pt 2pt 4pt #999;
      /* unfitted */
      background: var(--sklearn-color-unfitted-level-0);
      border: .5pt solid var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted span {
      /* fitted */
      background: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3);
    }

    .sk-estimator-doc-link:hover span {
      display: block;
    }

    /* "?"-specific style due to the `<a>` HTML tag */

    #sk-container-id-24 a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-background);
      border-radius: 1rem;
      height: 1rem;
      width: 1rem;
      text-decoration: none;
      /* unfitted */
      color: var(--sklearn-color-unfitted-level-1);
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
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    #sk-container-id-24 a.estimator_doc_link.fitted {
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      color: var(--sklearn-color-fitted-level-1);
    }

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      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    #sk-container-id-24 a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }
    </style><div id="sk-container-id-24" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-70" type="checkbox" checked><label for="sk-estimator-id-70" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>LinearRegression</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/dev/modules/generated/sklearn.linear_model.LinearRegression.html">?<span>Documentation for LinearRegression</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted"><pre>LinearRegression()</pre></div> </div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 38-39

رسم النتائج:

.. GENERATED FROM PYTHON SOURCE LINES 39-61

.. code-block:: Python


    segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]
    lc = LineCollection(segments, zorder=0)
    lc.set_array(np.ones(len(y)))
    lc.set_linewidths(np.full(n, 0.5))

    fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(12, 6))

    ax0.plot(x, y, "C0.", markersize=12)
    ax0.plot(x, y_, "C1.-", markersize=12)
    ax0.plot(x, lr.predict(x[:, np.newaxis]), "C2-")
    ax0.add_collection(lc)
    ax0.legend(("Training data", "Isotonic fit", "Linear fit"), loc="lower right")
    ax0.set_title("Isotonic regression fit on noisy data (n=%d)" % n)

    x_test = np.linspace(-10, 110, 1000)
    ax1.plot(x_test, ir.predict(x_test), "C1-")
    ax1.plot(ir.X_thresholds_, ir.y_thresholds_, "C1.", markersize=12)
    ax1.set_title("Prediction function (%d thresholds)" % len(ir.X_thresholds_))

    plt.show()




.. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_isotonic_regression_001.png
   :alt: Isotonic regression fit on noisy data (n=100), Prediction function (36 thresholds)
   :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_isotonic_regression_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 62-62

لاحظ أننا مررنا صراحةً `out_of_bounds="clip"` إلى منشئ `IsotonicRegression` للتحكم في طريقة استقراء النموذج خارج نطاق البيانات الملاحظة في مجموعة التدريب. يمكن رؤية هذا الاستقراء "القص" على رسم دالة القرار على الجانب الأيمن.


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

   **Total running time of the script:** (0 minutes 0.149 seconds)


.. _sphx_glr_download_auto_examples_miscellaneous_plot_isotonic_regression.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/main?urlpath=lab/tree/notebooks/auto_examples/miscellaneous/plot_isotonic_regression.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/miscellaneous/plot_isotonic_regression.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_isotonic_regression.zip <plot_isotonic_regression.zip>`


.. include:: plot_isotonic_regression.recommendations


.. only:: html

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

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