.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/decomposition/plot_varimax_fa.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` 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_decomposition_plot_varimax_fa.py: =============================================================== Factor Analysis (with rotation) to visualize patterns =============================================================== Investigating the Iris dataset, we see that sepal length, petal length and petal width are highly correlated. Sepal width is less redundant. Matrix decomposition techniques can uncover these latent patterns. Applying rotations to the resulting components does not inherently improve the predictive value of the derived latent space, but can help visualise their structure; here, for example, the varimax rotation, which is found by maximizing the squared variances of the weights, finds a structure where the second component only loads positively on sepal width. .. GENERATED FROM PYTHON SOURCE LINES 18-29 .. code-block:: Python # Authors: Jona Sassenhagen # License: BSD 3 clause import matplotlib.pyplot as plt import numpy as np from sklearn.datasets import load_iris from sklearn.decomposition import PCA, FactorAnalysis from sklearn.preprocessing import StandardScaler .. GENERATED FROM PYTHON SOURCE LINES 30-31 Load Iris data .. GENERATED FROM PYTHON SOURCE LINES 31-35 .. code-block:: Python data = load_iris() X = StandardScaler().fit_transform(data["data"]) feature_names = data["feature_names"] .. GENERATED FROM PYTHON SOURCE LINES 36-37 Plot covariance of Iris features .. GENERATED FROM PYTHON SOURCE LINES 37-50 .. code-block:: Python ax = plt.axes() im = ax.imshow(np.corrcoef(X.T), cmap="RdBu_r", vmin=-1, vmax=1) ax.set_xticks([0, 1, 2, 3]) ax.set_xticklabels(list(feature_names), rotation=90) ax.set_yticks([0, 1, 2, 3]) ax.set_yticklabels(list(feature_names)) plt.colorbar(im).ax.set_ylabel("$r$", rotation=0) ax.set_title("Iris feature correlation matrix") plt.tight_layout() .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_001.png :alt: Iris feature correlation matrix :srcset: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 51-52 Run factor analysis with Varimax rotation .. GENERATED FROM PYTHON SOURCE LINES 52-79 .. code-block:: Python n_comps = 2 methods = [ ("PCA", PCA()), ("Unrotated FA", FactorAnalysis()), ("Varimax FA", FactorAnalysis(rotation="varimax")), ] fig, axes = plt.subplots(ncols=len(methods), figsize=(10, 8), sharey=True) for ax, (method, fa) in zip(axes, methods): fa.set_params(n_components=n_comps) fa.fit(X) components = fa.components_.T print("\n\n %s :\n" % method) print(components) vmax = np.abs(components).max() ax.imshow(components, cmap="RdBu_r", vmax=vmax, vmin=-vmax) ax.set_yticks(np.arange(len(feature_names))) ax.set_yticklabels(feature_names) ax.set_title(str(method)) ax.set_xticks([0, 1]) ax.set_xticklabels(["Comp. 1", "Comp. 2"]) fig.suptitle("Factors") plt.tight_layout() plt.show() .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_002.png :alt: Factors, PCA, Unrotated FA, Varimax FA :srcset: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none PCA : [[ 0.52106591 0.37741762] [-0.26934744 0.92329566] [ 0.5804131 0.02449161] [ 0.56485654 0.06694199]] Unrotated FA : [[ 0.88096009 -0.4472869 ] [-0.41691605 -0.55390036] [ 0.99918858 0.01915283] [ 0.96228895 0.05840206]] Varimax FA : [[ 0.98633022 -0.05752333] [-0.16052385 -0.67443065] [ 0.90809432 0.41726413] [ 0.85857475 0.43847489]] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.438 seconds) .. _sphx_glr_download_auto_examples_decomposition_plot_varimax_fa.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/decomposition/plot_varimax_fa.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/decomposition/plot_varimax_fa.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_varimax_fa.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_varimax_fa.py ` .. include:: plot_varimax_fa.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_