.. _sphx_glr_auto_examples_classification_plot_lda.py:


====================================================================
Normal and Shrinkage Linear Discriminant Analysis for classification
====================================================================

Shows how shrinkage improves classification.



.. image:: /auto_examples/classification/images/sphx_glr_plot_lda_001.png
    :align: center





.. code-block:: python


    from __future__ import division

    import numpy as np
    import matplotlib.pyplot as plt

    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 = [], []
    n_features_range = range(1, n_features_max + 1, step)
    for n_features in n_features_range:
        score_clf1, score_clf2 = 0, 0
        for _ in range(n_averages):
            X, y = generate_data(n_train, n_features)

            clf1 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage='auto').fit(X, y)
            clf2 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage=None).fit(X, y)

            X, y = generate_data(n_test, n_features)
            score_clf1 += clf1.score(X, y)
            score_clf2 += clf2.score(X, y)

        acc_clf1.append(score_clf1 / n_averages)
        acc_clf2.append(score_clf2 / n_averages)

    features_samples_ratio = np.array(n_features_range) / n_train

    plt.plot(features_samples_ratio, acc_clf1, linewidth=2,
             label="Linear Discriminant Analysis with shrinkage", color='navy')
    plt.plot(features_samples_ratio, acc_clf2, linewidth=2,
             label="Linear Discriminant Analysis", color='gold')

    plt.xlabel('n_features / n_samples')
    plt.ylabel('Classification accuracy')

    plt.legend(loc=1, prop={'size': 12})
    plt.suptitle('Linear Discriminant Analysis vs. \
    shrinkage Linear Discriminant Analysis (1 discriminative feature)')
    plt.show()

**Total running time of the script:**
(0 minutes 5.694 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_lda.ipynb <plot_lda.ipynb>`