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

    Click :ref:`here <sphx_glr_download_auto_examples_neural_networks_plot_rbm_logistic_classification.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_neural_networks_plot_rbm_logistic_classification.py:


==============================================================
Restricted Boltzmann Machine features for digit classification
==============================================================

For greyscale image data where pixel values can be interpreted as degrees of
blackness on a white background, like handwritten digit recognition, the
Bernoulli Restricted Boltzmann machine model (:class:`BernoulliRBM
<sklearn.neural_network.BernoulliRBM>`) can perform effective non-linear
feature extraction.

In order to learn good latent representations from a small dataset, we
artificially generate more labeled data by perturbing the training data with
linear shifts of 1 pixel in each direction.

This example shows how to build a classification pipeline with a BernoulliRBM
feature extractor and a :class:`LogisticRegression
<sklearn.linear_model.LogisticRegression>` classifier. The hyperparameters
of the entire model (learning rate, hidden layer size, regularization)
were optimized by grid search, but the search is not reproduced here because
of runtime constraints.

Logistic regression on raw pixel values is presented for comparison. The
example shows that the features extracted by the BernoulliRBM help improve the
classification accuracy.



.. code-block:: python


    from __future__ import print_function

    print(__doc__)

    # Authors: Yann N. Dauphin, Vlad Niculae, Gabriel Synnaeve
    # License: BSD

    import numpy as np
    import matplotlib.pyplot as plt

    from scipy.ndimage import convolve
    from sklearn import linear_model, datasets, metrics
    from sklearn.model_selection import train_test_split
    from sklearn.neural_network import BernoulliRBM
    from sklearn.pipeline import Pipeline


    # #############################################################################
    # Setting up

    def nudge_dataset(X, Y):
        """
        This produces a dataset 5 times bigger than the original one,
        by moving the 8x8 images in X around by 1px to left, right, down, up
        """
        direction_vectors = [
            [[0, 1, 0],
             [0, 0, 0],
             [0, 0, 0]],

            [[0, 0, 0],
             [1, 0, 0],
             [0, 0, 0]],

            [[0, 0, 0],
             [0, 0, 1],
             [0, 0, 0]],

            [[0, 0, 0],
             [0, 0, 0],
             [0, 1, 0]]]

        shift = lambda x, w: convolve(x.reshape((8, 8)), mode='constant',
                                      weights=w).ravel()
        X = np.concatenate([X] +
                           [np.apply_along_axis(shift, 1, X, vector)
                            for vector in direction_vectors])
        Y = np.concatenate([Y for _ in range(5)], axis=0)
        return X, Y

    # Load Data
    digits = datasets.load_digits()
    X = np.asarray(digits.data, 'float32')
    X, Y = nudge_dataset(X, digits.target)
    X = (X - np.min(X, 0)) / (np.max(X, 0) + 0.0001)  # 0-1 scaling

    X_train, X_test, Y_train, Y_test = train_test_split(X, Y,
                                                        test_size=0.2,
                                                        random_state=0)

    # Models we will use
    logistic = linear_model.LogisticRegression()
    rbm = BernoulliRBM(random_state=0, verbose=True)

    classifier = Pipeline(steps=[('rbm', rbm), ('logistic', logistic)])

    # #############################################################################
    # Training

    # Hyper-parameters. These were set by cross-validation,
    # using a GridSearchCV. Here we are not performing cross-validation to
    # save time.
    rbm.learning_rate = 0.06
    rbm.n_iter = 20
    # More components tend to give better prediction performance, but larger
    # fitting time
    rbm.n_components = 100
    logistic.C = 6000.0

    # Training RBM-Logistic Pipeline
    classifier.fit(X_train, Y_train)

    # Training Logistic regression
    logistic_classifier = linear_model.LogisticRegression(C=100.0)
    logistic_classifier.fit(X_train, Y_train)

    # #############################################################################
    # Evaluation

    print()
    print("Logistic regression using RBM features:\n%s\n" % (
        metrics.classification_report(
            Y_test,
            classifier.predict(X_test))))

    print("Logistic regression using raw pixel features:\n%s\n" % (
        metrics.classification_report(
            Y_test,
            logistic_classifier.predict(X_test))))

    # #############################################################################
    # Plotting

    plt.figure(figsize=(4.2, 4))
    for i, comp in enumerate(rbm.components_):
        plt.subplot(10, 10, i + 1)
        plt.imshow(comp.reshape((8, 8)), cmap=plt.cm.gray_r,
                   interpolation='nearest')
        plt.xticks(())
        plt.yticks(())
    plt.suptitle('100 components extracted by RBM', fontsize=16)
    plt.subplots_adjust(0.08, 0.02, 0.92, 0.85, 0.08, 0.23)

    plt.show()

**Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_neural_networks_plot_rbm_logistic_classification.py:


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