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

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

.. _sphx_glr_auto_examples_cluster_plot_feature_agglomeration_vs_univariate_selection.py:


==============================================
Feature agglomeration vs. univariate selection
==============================================

This example compares 2 dimensionality reduction strategies:

- univariate feature selection with Anova

- feature agglomeration with Ward hierarchical clustering

Both methods are compared in a regression problem using
a BayesianRidge as supervised estimator.



.. code-block:: python


    # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
    # License: BSD 3 clause

    print(__doc__)

    import shutil
    import tempfile

    import numpy as np
    import matplotlib.pyplot as plt
    from scipy import linalg, ndimage

    from sklearn.feature_extraction.image import grid_to_graph
    from sklearn import feature_selection
    from sklearn.cluster import FeatureAgglomeration
    from sklearn.linear_model import BayesianRidge
    from sklearn.pipeline import Pipeline
    from sklearn.utils.joblib import Memory
    from sklearn.model_selection import GridSearchCV
    from sklearn.model_selection import KFold

    # #############################################################################
    # Generate data
    n_samples = 200
    size = 40  # image size
    roi_size = 15
    snr = 5.
    np.random.seed(0)
    mask = np.ones([size, size], dtype=np.bool)

    coef = np.zeros((size, size))
    coef[0:roi_size, 0:roi_size] = -1.
    coef[-roi_size:, -roi_size:] = 1.

    X = np.random.randn(n_samples, size ** 2)
    for x in X:  # smooth data
        x[:] = ndimage.gaussian_filter(x.reshape(size, size), sigma=1.0).ravel()
    X -= X.mean(axis=0)
    X /= X.std(axis=0)

    y = np.dot(X, coef.ravel())
    noise = np.random.randn(y.shape[0])
    noise_coef = (linalg.norm(y, 2) / np.exp(snr / 20.)) / linalg.norm(noise, 2)
    y += noise_coef * noise  # add noise

    # #############################################################################
    # Compute the coefs of a Bayesian Ridge with GridSearch
    cv = KFold(2)  # cross-validation generator for model selection
    ridge = BayesianRidge()
    cachedir = tempfile.mkdtemp()
    mem = Memory(cachedir=cachedir, verbose=1)

    # Ward agglomeration followed by BayesianRidge
    connectivity = grid_to_graph(n_x=size, n_y=size)
    ward = FeatureAgglomeration(n_clusters=10, connectivity=connectivity,
                                memory=mem)
    clf = Pipeline([('ward', ward), ('ridge', ridge)])
    # Select the optimal number of parcels with grid search
    clf = GridSearchCV(clf, {'ward__n_clusters': [10, 20, 30]}, n_jobs=1, cv=cv)
    clf.fit(X, y)  # set the best parameters
    coef_ = clf.best_estimator_.steps[-1][1].coef_
    coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_)
    coef_agglomeration_ = coef_.reshape(size, size)

    # Anova univariate feature selection followed by BayesianRidge
    f_regression = mem.cache(feature_selection.f_regression)  # caching function
    anova = feature_selection.SelectPercentile(f_regression)
    clf = Pipeline([('anova', anova), ('ridge', ridge)])
    # Select the optimal percentage of features with grid search
    clf = GridSearchCV(clf, {'anova__percentile': [5, 10, 20]}, cv=cv)
    clf.fit(X, y)  # set the best parameters
    coef_ = clf.best_estimator_.steps[-1][1].coef_
    coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_.reshape(1, -1))
    coef_selection_ = coef_.reshape(size, size)

    # #############################################################################
    # Inverse the transformation to plot the results on an image
    plt.close('all')
    plt.figure(figsize=(7.3, 2.7))
    plt.subplot(1, 3, 1)
    plt.imshow(coef, interpolation="nearest", cmap=plt.cm.RdBu_r)
    plt.title("True weights")
    plt.subplot(1, 3, 2)
    plt.imshow(coef_selection_, interpolation="nearest", cmap=plt.cm.RdBu_r)
    plt.title("Feature Selection")
    plt.subplot(1, 3, 3)
    plt.imshow(coef_agglomeration_, interpolation="nearest", cmap=plt.cm.RdBu_r)
    plt.title("Feature Agglomeration")
    plt.subplots_adjust(0.04, 0.0, 0.98, 0.94, 0.16, 0.26)
    plt.show()

    # Attempt to remove the temporary cachedir, but don't worry if it fails
    shutil.rmtree(cachedir, ignore_errors=True)

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


.. _sphx_glr_download_auto_examples_cluster_plot_feature_agglomeration_vs_univariate_selection.py:


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 .. container:: sphx-glr-footer
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     :download:`Download Jupyter notebook: plot_feature_agglomeration_vs_univariate_selection.ipynb <plot_feature_agglomeration_vs_univariate_selection.ipynb>`


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