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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/neural_networks/plot_rbm_logistic_classification.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_neural_networks_plot_rbm_logistic_classification.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_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.

.. GENERATED FROM PYTHON SOURCE LINES 13-17

.. code-block:: default


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








.. GENERATED FROM PYTHON SOURCE LINES 18-24

Generate data
-------------

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.

.. GENERATED FROM PYTHON SOURCE LINES 24-62

.. code-block:: default


    import numpy as np
    from scipy.ndimage import convolve

    from sklearn import datasets
    from sklearn.model_selection import train_test_split
    from sklearn.preprocessing import minmax_scale


    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]],
        ]

        def shift(x, w):
            return 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


    X, y = datasets.load_digits(return_X_y=True)
    X = np.asarray(X, "float32")
    X, Y = nudge_dataset(X, y)
    X = minmax_scale(X, feature_range=(0, 1))  # 0-1 scaling

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








.. GENERATED FROM PYTHON SOURCE LINES 63-69

Models definition
-----------------

We build a classification pipeline with a BernoulliRBM feature extractor and
a :class:`LogisticRegression <sklearn.linear_model.LogisticRegression>`
classifier.

.. GENERATED FROM PYTHON SOURCE LINES 69-79

.. code-block:: default


    from sklearn import linear_model
    from sklearn.neural_network import BernoulliRBM
    from sklearn.pipeline import Pipeline

    logistic = linear_model.LogisticRegression(solver="newton-cg", tol=1)
    rbm = BernoulliRBM(random_state=0, verbose=True)

    rbm_features_classifier = Pipeline(steps=[("rbm", rbm), ("logistic", logistic)])








.. GENERATED FROM PYTHON SOURCE LINES 80-86

Training
--------

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.

.. GENERATED FROM PYTHON SOURCE LINES 86-108

.. code-block:: default


    from sklearn.base import clone

    # 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 = 10

    # More components tend to give better prediction performance, but larger
    # fitting time
    rbm.n_components = 100
    logistic.C = 6000

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

    # Training the Logistic regression classifier directly on the pixel
    raw_pixel_classifier = clone(logistic)
    raw_pixel_classifier.C = 100.0
    raw_pixel_classifier.fit(X_train, Y_train)





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

 .. code-block:: none

    [BernoulliRBM] Iteration 1, pseudo-likelihood = -25.57, time = 0.08s
    [BernoulliRBM] Iteration 2, pseudo-likelihood = -23.68, time = 0.15s
    [BernoulliRBM] Iteration 3, pseudo-likelihood = -22.88, time = 0.15s
    [BernoulliRBM] Iteration 4, pseudo-likelihood = -21.91, time = 0.15s
    [BernoulliRBM] Iteration 5, pseudo-likelihood = -21.79, time = 0.15s
    [BernoulliRBM] Iteration 6, pseudo-likelihood = -20.96, time = 0.15s
    [BernoulliRBM] Iteration 7, pseudo-likelihood = -20.80, time = 0.15s
    [BernoulliRBM] Iteration 8, pseudo-likelihood = -20.63, time = 0.15s
    [BernoulliRBM] Iteration 9, pseudo-likelihood = -20.38, time = 0.15s
    [BernoulliRBM] Iteration 10, pseudo-likelihood = -20.19, time = 0.14s


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-59 {color: black;}#sk-container-id-59 pre{padding: 0;}#sk-container-id-59 div.sk-toggleable {background-color: white;}#sk-container-id-59 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-59 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-59 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-59 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-59 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-59 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-59 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-59 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-59 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-59 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-59 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-59 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-59 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-59 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-59 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-59 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-59 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-59 div.sk-item {position: relative;z-index: 1;}#sk-container-id-59 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-59 div.sk-item::before, #sk-container-id-59 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-59 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-59 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-59 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-59 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-59 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-59 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-59 div.sk-label-container {text-align: center;}#sk-container-id-59 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` 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-59 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-59" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>LogisticRegression(C=100.0, solver=&#x27;newton-cg&#x27;, tol=1)</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 sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-247" type="checkbox" checked><label for="sk-estimator-id-247" class="sk-toggleable__label sk-toggleable__label-arrow">LogisticRegression</label><div class="sk-toggleable__content"><pre>LogisticRegression(C=100.0, solver=&#x27;newton-cg&#x27;, tol=1)</pre></div></div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 109-111

Evaluation
----------

.. GENERATED FROM PYTHON SOURCE LINES 111-120

.. code-block:: default


    from sklearn import metrics

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





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

 .. code-block:: none

    Logistic regression using RBM features:
                  precision    recall  f1-score   support

               0       0.99      0.98      0.99       174
               1       0.89      0.92      0.91       184
               2       0.92      0.95      0.93       166
               3       0.94      0.89      0.91       194
               4       0.95      0.94      0.94       186
               5       0.93      0.92      0.92       181
               6       0.98      0.96      0.97       207
               7       0.93      0.99      0.96       154
               8       0.89      0.88      0.89       182
               9       0.88      0.90      0.89       169

        accuracy                           0.93      1797
       macro avg       0.93      0.93      0.93      1797
    weighted avg       0.93      0.93      0.93      1797






.. GENERATED FROM PYTHON SOURCE LINES 121-127

.. code-block:: default

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





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

 .. code-block:: none

    Logistic regression using raw pixel features:
                  precision    recall  f1-score   support

               0       0.90      0.92      0.91       174
               1       0.59      0.57      0.58       184
               2       0.75      0.85      0.80       166
               3       0.77      0.77      0.77       194
               4       0.82      0.83      0.83       186
               5       0.76      0.77      0.77       181
               6       0.90      0.87      0.89       207
               7       0.85      0.88      0.87       154
               8       0.68      0.57      0.62       182
               9       0.73      0.76      0.75       169

        accuracy                           0.78      1797
       macro avg       0.78      0.78      0.78      1797
    weighted avg       0.78      0.78      0.78      1797






.. GENERATED FROM PYTHON SOURCE LINES 128-130

The features extracted by the BernoulliRBM help improve the classification
accuracy with respect to the logistic regression on raw pixels.

.. GENERATED FROM PYTHON SOURCE LINES 132-134

Plotting
--------

.. GENERATED FROM PYTHON SOURCE LINES 134-147

.. code-block:: default


    import matplotlib.pyplot as plt

    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()



.. image-sg:: /auto_examples/neural_networks/images/sphx_glr_plot_rbm_logistic_classification_001.png
   :alt: 100 components extracted by RBM
   :srcset: /auto_examples/neural_networks/images/sphx_glr_plot_rbm_logistic_classification_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 3.972 seconds)


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