.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/classification/plot_lda.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_classification_plot_lda.py: =========================================================================== Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification =========================================================================== This example illustrates how the Ledoit-Wolf and Oracle Approximating Shrinkage (OAS) estimators of covariance can improve classification. .. GENERATED FROM PYTHON SOURCE LINES 10-108 .. image-sg:: /auto_examples/classification/images/sphx_glr_plot_lda_001.png :alt: LDA (Linear Discriminant Analysis) vs. LDA with Ledoit Wolf vs. LDA with OAS (1 discriminative feature) :srcset: /auto_examples/classification/images/sphx_glr_plot_lda_001.png :class: sphx-glr-single-img .. code-block:: Python # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.pyplot as plt import numpy as np from sklearn.covariance import OAS from sklearn.datasets import make_blobs from sklearn.discriminant_analysis import LinearDiscriminantAnalysis n_train = 20 # samples for training n_test = 200 # samples for testing n_averages = 50 # how often to repeat classification n_features_max = 75 # maximum number of features step = 4 # step size for the calculation def generate_data(n_samples, n_features): """Generate random blob-ish data with noisy features. This returns an array of input data with shape `(n_samples, n_features)` and an array of `n_samples` target labels. Only one feature contains discriminative information, the other features contain only noise. """ X, y = make_blobs(n_samples=n_samples, n_features=1, centers=[[-2], [2]]) # add non-discriminative features if n_features > 1: X = np.hstack([X, np.random.randn(n_samples, n_features - 1)]) return X, y acc_clf1, acc_clf2, acc_clf3 = [], [], [] n_features_range = range(1, n_features_max + 1, step) for n_features in n_features_range: score_clf1, score_clf2, score_clf3 = 0, 0, 0 for _ in range(n_averages): X, y = generate_data(n_train, n_features) clf1 = LinearDiscriminantAnalysis(solver="lsqr", shrinkage=None).fit(X, y) clf2 = LinearDiscriminantAnalysis(solver="lsqr", shrinkage="auto").fit(X, y) oa = OAS(store_precision=False, assume_centered=False) clf3 = LinearDiscriminantAnalysis(solver="lsqr", covariance_estimator=oa).fit( X, y ) X, y = generate_data(n_test, n_features) score_clf1 += clf1.score(X, y) score_clf2 += clf2.score(X, y) score_clf3 += clf3.score(X, y) acc_clf1.append(score_clf1 / n_averages) acc_clf2.append(score_clf2 / n_averages) acc_clf3.append(score_clf3 / n_averages) features_samples_ratio = np.array(n_features_range) / n_train plt.plot( features_samples_ratio, acc_clf1, linewidth=2, label="LDA", color="gold", linestyle="solid", ) plt.plot( features_samples_ratio, acc_clf2, linewidth=2, label="LDA with Ledoit Wolf", color="navy", linestyle="dashed", ) plt.plot( features_samples_ratio, acc_clf3, linewidth=2, label="LDA with OAS", color="red", linestyle="dotted", ) plt.xlabel("n_features / n_samples") plt.ylabel("Classification accuracy") plt.legend(loc="lower left") plt.ylim((0.65, 1.0)) plt.suptitle( "LDA (Linear Discriminant Analysis) vs. " + "\n" + "LDA with Ledoit Wolf vs. " + "\n" + "LDA with OAS (1 discriminative feature)" ) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 9.629 seconds) .. _sphx_glr_download_auto_examples_classification_plot_lda.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/main?urlpath=lab/tree/notebooks/auto_examples/classification/plot_lda.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/index.html?path=auto_examples/classification/plot_lda.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_lda.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_lda.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_lda.zip ` .. include:: plot_lda.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_