.. _sphx_glr_auto_examples_linear_model_plot_ransac.py:


===========================================
Robust linear model estimation using RANSAC
===========================================

In this example we see how to robustly fit a linear model to faulty data using
the RANSAC algorithm.




.. image:: /auto_examples/linear_model/images/sphx_glr_plot_ransac_001.png
    :align: center


.. rst-class:: sphx-glr-script-out

 Out::

      Estimated coefficients (true, normal, RANSAC):
    82.1903908408 [ 54.17236387] [ 82.08533159]




|


.. code-block:: python

    import numpy as np
    from matplotlib import pyplot as plt

    from sklearn import linear_model, datasets


    n_samples = 1000
    n_outliers = 50


    X, y, coef = datasets.make_regression(n_samples=n_samples, n_features=1,
                                          n_informative=1, noise=10,
                                          coef=True, random_state=0)

    # Add outlier data
    np.random.seed(0)
    X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))
    y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)

    # Fit line using all data
    model = linear_model.LinearRegression()
    model.fit(X, y)

    # Robustly fit linear model with RANSAC algorithm
    model_ransac = linear_model.RANSACRegressor(linear_model.LinearRegression())
    model_ransac.fit(X, y)
    inlier_mask = model_ransac.inlier_mask_
    outlier_mask = np.logical_not(inlier_mask)

    # Predict data of estimated models
    line_X = np.arange(-5, 5)
    line_y = model.predict(line_X[:, np.newaxis])
    line_y_ransac = model_ransac.predict(line_X[:, np.newaxis])

    # Compare estimated coefficients
    print("Estimated coefficients (true, normal, RANSAC):")
    print(coef, model.coef_, model_ransac.estimator_.coef_)

    lw = 2
    plt.scatter(X[inlier_mask], y[inlier_mask], color='yellowgreen', marker='.',
                label='Inliers')
    plt.scatter(X[outlier_mask], y[outlier_mask], color='gold', marker='.',
                label='Outliers')
    plt.plot(line_X, line_y, color='navy', linestyle='-', linewidth=lw,
             label='Linear regressor')
    plt.plot(line_X, line_y_ransac, color='cornflowerblue', linestyle='-',
             linewidth=lw, label='RANSAC regressor')
    plt.legend(loc='lower right')
    plt.show()

**Total running time of the script:**
(0 minutes 0.126 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

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