.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/linear_model/plot_nnls.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_linear_model_plot_nnls.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_linear_model_plot_nnls.py:


==========================
Non-negative least squares
==========================

In this example, we fit a linear model with positive constraints on the
regression coefficients and compare the estimated coefficients to a classic
linear regression.

.. GENERATED FROM PYTHON SOURCE LINES 11-17

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.metrics import r2_score








.. GENERATED FROM PYTHON SOURCE LINES 18-19

Generate some random data

.. GENERATED FROM PYTHON SOURCE LINES 19-31

.. code-block:: Python

    np.random.seed(42)

    n_samples, n_features = 200, 50
    X = np.random.randn(n_samples, n_features)
    true_coef = 3 * np.random.randn(n_features)
    # Threshold coefficients to render them non-negative
    true_coef[true_coef < 0] = 0
    y = np.dot(X, true_coef)

    # Add some noise
    y += 5 * np.random.normal(size=(n_samples,))








.. GENERATED FROM PYTHON SOURCE LINES 32-33

Split the data in train set and test set

.. GENERATED FROM PYTHON SOURCE LINES 33-37

.. code-block:: Python

    from sklearn.model_selection import train_test_split

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Fit the Non-Negative least squares.

.. GENERATED FROM PYTHON SOURCE LINES 39-46

.. code-block:: Python

    from sklearn.linear_model import LinearRegression

    reg_nnls = LinearRegression(positive=True)
    y_pred_nnls = reg_nnls.fit(X_train, y_train).predict(X_test)
    r2_score_nnls = r2_score(y_test, y_pred_nnls)
    print("NNLS R2 score", r2_score_nnls)





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

 .. code-block:: none

    NNLS R2 score 0.8225220806196526




.. GENERATED FROM PYTHON SOURCE LINES 47-48

Fit an OLS.

.. GENERATED FROM PYTHON SOURCE LINES 48-54

.. code-block:: Python

    reg_ols = LinearRegression()
    y_pred_ols = reg_ols.fit(X_train, y_train).predict(X_test)
    r2_score_ols = r2_score(y_test, y_pred_ols)
    print("OLS R2 score", r2_score_ols)






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

 .. code-block:: none

    OLS R2 score 0.7436926291700354




.. GENERATED FROM PYTHON SOURCE LINES 55-59

Comparing the regression coefficients between OLS and NNLS, we can observe
they are highly correlated (the dashed line is the identity relation),
but the non-negative constraint shrinks some to 0.
The Non-Negative Least squares inherently yield sparse results.

.. GENERATED FROM PYTHON SOURCE LINES 59-70

.. code-block:: Python


    fig, ax = plt.subplots()
    ax.plot(reg_ols.coef_, reg_nnls.coef_, linewidth=0, marker=".")

    low_x, high_x = ax.get_xlim()
    low_y, high_y = ax.get_ylim()
    low = max(low_x, low_y)
    high = min(high_x, high_y)
    ax.plot([low, high], [low, high], ls="--", c=".3", alpha=0.5)
    ax.set_xlabel("OLS regression coefficients", fontweight="bold")
    ax.set_ylabel("NNLS regression coefficients", fontweight="bold")



.. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_nnls_001.png
   :alt: plot nnls
   :srcset: /auto_examples/linear_model/images/sphx_glr_plot_nnls_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(55.847222222222214, 0.5, 'NNLS regression coefficients')




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

   **Total running time of the script:** (0 minutes 0.077 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_nnls.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/linear_model/plot_nnls.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/linear_model/plot_nnls.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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


.. include:: plot_nnls.recommendations


.. only:: html

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

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