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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_classification_plot_lda.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

Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification

This example illustrates how the Ledoit-Wolf and Oracle Shrinkage Approximating (OAS) estimators of covariance can improve classification.

.. 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





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 7.242 seconds)


.. 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/1.3.X?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/?path=auto_examples/classification/plot_lda.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-python

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

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_