.. _sphx_glr_auto_examples_neighbors_plot_digits_kde_sampling.py:


=========================
Kernel Density Estimation
=========================

This example shows how kernel density estimation (KDE), a powerful
non-parametric density estimation technique, can be used to learn
a generative model for a dataset.  With this generative model in place,
new samples can be drawn.  These new samples reflect the underlying model
of the data.




.. image:: /auto_examples/neighbors/images/sphx_glr_plot_digits_kde_sampling_001.png
    :align: center


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

 Out::

    best bandwidth: 3.79269019073225




|


.. code-block:: python


    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.datasets import load_digits
    from sklearn.neighbors import KernelDensity
    from sklearn.decomposition import PCA
    from sklearn.model_selection import GridSearchCV

    # load the data
    digits = load_digits()
    data = digits.data

    # project the 64-dimensional data to a lower dimension
    pca = PCA(n_components=15, whiten=False)
    data = pca.fit_transform(digits.data)

    # use grid search cross-validation to optimize the bandwidth
    params = {'bandwidth': np.logspace(-1, 1, 20)}
    grid = GridSearchCV(KernelDensity(), params)
    grid.fit(data)

    print("best bandwidth: {0}".format(grid.best_estimator_.bandwidth))

    # use the best estimator to compute the kernel density estimate
    kde = grid.best_estimator_

    # sample 44 new points from the data
    new_data = kde.sample(44, random_state=0)
    new_data = pca.inverse_transform(new_data)

    # turn data into a 4x11 grid
    new_data = new_data.reshape((4, 11, -1))
    real_data = digits.data[:44].reshape((4, 11, -1))

    # plot real digits and resampled digits
    fig, ax = plt.subplots(9, 11, subplot_kw=dict(xticks=[], yticks=[]))
    for j in range(11):
        ax[4, j].set_visible(False)
        for i in range(4):
            im = ax[i, j].imshow(real_data[i, j].reshape((8, 8)),
                                 cmap=plt.cm.binary, interpolation='nearest')
            im.set_clim(0, 16)
            im = ax[i + 5, j].imshow(new_data[i, j].reshape((8, 8)),
                                     cmap=plt.cm.binary, interpolation='nearest')
            im.set_clim(0, 16)

    ax[0, 5].set_title('Selection from the input data')
    ax[5, 5].set_title('"New" digits drawn from the kernel density model')

    plt.show()

**Total running time of the script:** ( 0 minutes  10.950 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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