.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_linear_model_plot_sparse_logistic_regression_mnist.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_linear_model_plot_sparse_logistic_regression_mnist.py:


=====================================================
MNIST classification using multinomial logistic + L1
=====================================================

Here we fit a multinomial logistic regression with L1 penalty on a subset of
the MNIST digits classification task. We use the SAGA algorithm for this
purpose: this a solver that is fast when the number of samples is significantly
larger than the number of features and is able to finely optimize non-smooth
objective functions which is the case with the l1-penalty. Test accuracy
reaches > 0.8, while weight vectors remains *sparse* and therefore more easily
*interpretable*.

Note that this accuracy of this l1-penalized linear model is significantly
below what can be reached by an l2-penalized linear model or a non-linear
multi-layer perceptron model on this dataset.



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_sparse_logistic_regression_mnist_001.png
    :alt: Classification vector for...
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    Sparsity with L1 penalty: 79.95%
    Test score with L1 penalty: 0.8322
    Example run in 23.797 s






|


.. code-block:: default

    import time
    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import fetch_openml
    from sklearn.linear_model import LogisticRegression
    from sklearn.model_selection import train_test_split
    from sklearn.preprocessing import StandardScaler
    from sklearn.utils import check_random_state

    print(__doc__)

    # Author: Arthur Mensch <arthur.mensch@m4x.org>
    # License: BSD 3 clause

    # Turn down for faster convergence
    t0 = time.time()
    train_samples = 5000

    # Load data from https://www.openml.org/d/554
    X, y = fetch_openml('mnist_784', version=1, return_X_y=True)

    random_state = check_random_state(0)
    permutation = random_state.permutation(X.shape[0])
    X = X[permutation]
    y = y[permutation]
    X = X.reshape((X.shape[0], -1))

    X_train, X_test, y_train, y_test = train_test_split(
        X, y, train_size=train_samples, test_size=10000)

    scaler = StandardScaler()
    X_train = scaler.fit_transform(X_train)
    X_test = scaler.transform(X_test)

    # Turn up tolerance for faster convergence
    clf = LogisticRegression(
        C=50. / train_samples, penalty='l1', solver='saga', tol=0.1
    )
    clf.fit(X_train, y_train)
    sparsity = np.mean(clf.coef_ == 0) * 100
    score = clf.score(X_test, y_test)
    # print('Best C % .4f' % clf.C_)
    print("Sparsity with L1 penalty: %.2f%%" % sparsity)
    print("Test score with L1 penalty: %.4f" % score)

    coef = clf.coef_.copy()
    plt.figure(figsize=(10, 5))
    scale = np.abs(coef).max()
    for i in range(10):
        l1_plot = plt.subplot(2, 5, i + 1)
        l1_plot.imshow(coef[i].reshape(28, 28), interpolation='nearest',
                       cmap=plt.cm.RdBu, vmin=-scale, vmax=scale)
        l1_plot.set_xticks(())
        l1_plot.set_yticks(())
        l1_plot.set_xlabel('Class %i' % i)
    plt.suptitle('Classification vector for...')

    run_time = time.time() - t0
    print('Example run in %.3f s' % run_time)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  23.877 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_sparse_logistic_regression_mnist.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/0.23.X?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_sparse_logistic_regression_mnist.ipynb
      :width: 150 px


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

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



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

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


.. only:: html

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

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