79 lines
2.0 KiB
Python
79 lines
2.0 KiB
Python
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"""
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===========================================
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Robust linear model estimation using RANSAC
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===========================================
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In this example, we see how to robustly fit a linear model to faulty data using
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the :ref:`RANSAC <ransac_regression>` algorithm.
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The ordinary linear regressor is sensitive to outliers, and the fitted line can
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easily be skewed away from the true underlying relationship of data.
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The RANSAC regressor automatically splits the data into inliers and outliers,
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and the fitted line is determined only by the identified inliers.
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"""
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import numpy as np
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from matplotlib import pyplot as plt
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from sklearn import datasets, linear_model
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n_samples = 1000
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n_outliers = 50
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X, y, coef = datasets.make_regression(
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n_samples=n_samples,
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n_features=1,
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n_informative=1,
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noise=10,
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coef=True,
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random_state=0,
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)
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# Add outlier data
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np.random.seed(0)
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X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))
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y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)
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# Fit line using all data
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lr = linear_model.LinearRegression()
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lr.fit(X, y)
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# Robustly fit linear model with RANSAC algorithm
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ransac = linear_model.RANSACRegressor()
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ransac.fit(X, y)
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inlier_mask = ransac.inlier_mask_
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outlier_mask = np.logical_not(inlier_mask)
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# Predict data of estimated models
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line_X = np.arange(X.min(), X.max())[:, np.newaxis]
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line_y = lr.predict(line_X)
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line_y_ransac = ransac.predict(line_X)
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# Compare estimated coefficients
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print("Estimated coefficients (true, linear regression, RANSAC):")
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print(coef, lr.coef_, ransac.estimator_.coef_)
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lw = 2
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plt.scatter(
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X[inlier_mask], y[inlier_mask], color="yellowgreen", marker=".", label="Inliers"
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)
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plt.scatter(
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X[outlier_mask], y[outlier_mask], color="gold", marker=".", label="Outliers"
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)
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plt.plot(line_X, line_y, color="navy", linewidth=lw, label="Linear regressor")
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plt.plot(
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line_X,
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line_y_ransac,
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color="cornflowerblue",
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linewidth=lw,
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label="RANSAC regressor",
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)
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plt.legend(loc="lower right")
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plt.xlabel("Input")
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plt.ylabel("Response")
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plt.show()
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