.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/cluster/plot_feature_agglomeration_vs_univariate_selection.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_cluster_plot_feature_agglomeration_vs_univariate_selection.py>`
to download the full example code or to run this example in your browser via JupyterLite or Binder
.. 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.
.. GENERATED FROM PYTHON SOURCE LINES 16-20
.. code-block:: Python
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# License: BSD 3 clause
.. GENERATED FROM PYTHON SOURCE LINES 21-36
.. code-block:: Python
import shutil
import tempfile
import matplotlib.pyplot as plt
import numpy as np
from joblib import Memory
from scipy import linalg, ndimage
from sklearn import feature_selection
from sklearn.cluster import FeatureAgglomeration
from sklearn.feature_extraction.image import grid_to_graph
from sklearn.linear_model import BayesianRidge
from sklearn.model_selection import GridSearchCV, KFold
from sklearn.pipeline import Pipeline
.. GENERATED FROM PYTHON SOURCE LINES 37-38
Set parameters
.. GENERATED FROM PYTHON SOURCE LINES 38-44
.. code-block:: Python
n_samples = 200
size = 40 # image size
roi_size = 15
snr = 5.0
np.random.seed(0)
.. GENERATED FROM PYTHON SOURCE LINES 45-46
Generate data
.. GENERATED FROM PYTHON SOURCE LINES 46-58
.. code-block:: Python
coef = np.zeros((size, size))
coef[0:roi_size, 0:roi_size] = -1.0
coef[-roi_size:, -roi_size:] = 1.0
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())
.. GENERATED FROM PYTHON SOURCE LINES 59-60
add noise
.. GENERATED FROM PYTHON SOURCE LINES 60-64
.. code-block:: Python
noise = np.random.randn(y.shape[0])
noise_coef = (linalg.norm(y, 2) / np.exp(snr / 20.0)) / linalg.norm(noise, 2)
y += noise_coef * noise
.. GENERATED FROM PYTHON SOURCE LINES 65-66
Compute the coefs of a Bayesian Ridge with GridSearch
.. GENERATED FROM PYTHON SOURCE LINES 66-71
.. code-block:: Python
cv = KFold(2) # cross-validation generator for model selection
ridge = BayesianRidge()
cachedir = tempfile.mkdtemp()
mem = Memory(location=cachedir, verbose=1)
.. GENERATED FROM PYTHON SOURCE LINES 72-73
Ward agglomeration followed by BayesianRidge
.. GENERATED FROM PYTHON SOURCE LINES 73-83
.. code-block:: Python
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)
.. rst-class:: sphx-glr-script-out
.. code-block:: none
________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[-0.451933, ..., -0.675318],
...,
[ 0.275706, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[ 0.905206, ..., 0.161245],
...,
[-0.849835, ..., -1.091621]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[ 0.905206, ..., -0.675318],
...,
[-0.849835, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.0s, 0.0min
.. GENERATED FROM PYTHON SOURCE LINES 84-85
Anova univariate feature selection followed by BayesianRidge
.. GENERATED FROM PYTHON SOURCE LINES 85-95
.. code-block:: Python
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)
.. rst-class:: sphx-glr-script-out
.. code-block:: none
________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[-0.451933, ..., 0.275706],
...,
[-0.675318, ..., -1.085711]]),
array([ 25.267703, ..., -25.026711]))
_____________________________________________________f_regression - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[ 0.905206, ..., -0.849835],
...,
[ 0.161245, ..., -1.091621]]),
array([ -27.447268, ..., -112.638768]))
_____________________________________________________f_regression - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[ 0.905206, ..., -0.849835],
...,
[-0.675318, ..., -1.085711]]),
array([-27.447268, ..., -25.026711]))
_____________________________________________________f_regression - 0.0s, 0.0min
.. GENERATED FROM PYTHON SOURCE LINES 96-97
Inverse the transformation to plot the results on an image
.. GENERATED FROM PYTHON SOURCE LINES 97-111
.. code-block:: Python
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()
.. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_feature_agglomeration_vs_univariate_selection_001.png
:alt: True weights, Feature Selection, Feature Agglomeration
:srcset: /auto_examples/cluster/images/sphx_glr_plot_feature_agglomeration_vs_univariate_selection_001.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 112-113
Attempt to remove the temporary cachedir, but don't worry if it fails
.. GENERATED FROM PYTHON SOURCE LINES 113-114
.. code-block:: Python
shutil.rmtree(cachedir, ignore_errors=True)
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 0.499 seconds)
.. _sphx_glr_download_auto_examples_cluster_plot_feature_agglomeration_vs_univariate_selection.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: binder-badge
.. image:: images/binder_badge_logo.svg
:target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.4.X?urlpath=lab/tree/notebooks/auto_examples/cluster/plot_feature_agglomeration_vs_univariate_selection.ipynb
:alt: Launch binder
:width: 150 px
.. container:: lite-badge
.. image:: images/jupyterlite_badge_logo.svg
:target: ../../lite/lab/?path=auto_examples/cluster/plot_feature_agglomeration_vs_univariate_selection.ipynb
:alt: Launch JupyterLite
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_feature_agglomeration_vs_univariate_selection.ipynb <plot_feature_agglomeration_vs_univariate_selection.ipynb>`
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_feature_agglomeration_vs_univariate_selection.py <plot_feature_agglomeration_vs_univariate_selection.py>`
.. include:: plot_feature_agglomeration_vs_univariate_selection.recommendations
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_