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Support Vector Regression (SVR) using linear and non-linear kernels#

Toy example of 1D regression using linear, polynomial and RBF kernels.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearn.svmimport SVR

Generate sample data#

X = np.sort (5 * np.random.rand (40, 1), axis=0)
y = np.sin (X).ravel()
# add noise to targets
y[::5] += 3 * (0.5 - np.random.rand (8))

Fit regression model#

svr_rbf = SVR (kernel="rbf", C=100, gamma=0.1, epsilon=0.1)
svr_lin = SVR (kernel="linear", C=100, gamma="auto")
svr_poly = SVR (kernel="poly", C=100, gamma="auto", degree=3, epsilon=0.1, coef0=1)

Look at the results#

lw = 2
svrs = [svr_rbf, svr_lin, svr_poly]
kernel_label = ["RBF", "Linear", "Polynomial"]
model_color = ["m", "c", "g"]
fig, axes = plt.subplots (nrows=1, ncols=3, figsize=(15, 10), sharey=True)
for ix, svr in enumerate(svrs):
 axes[ix].plot(
 X,
 svr.fit(X, y).predict(X),
 color=model_color[ix],
 lw=lw,
 label="{} model".format(kernel_label[ix]),
 )
 axes[ix].scatter(
 X[svr.support_],
 y[svr.support_],
 facecolor="none",
 edgecolor=model_color[ix],
 s=50,
 label="{} support vectors".format(kernel_label[ix]),
 )
 axes[ix].scatter(
 X[np.setdiff1d (np.arange (len(X)), svr.support_)],
 y[np.setdiff1d (np.arange (len(X)), svr.support_)],
 facecolor="none",
 edgecolor="k",
 s=50,
 label="other training data",
 )
 axes[ix].legend(
 loc="upper center",
 bbox_to_anchor=(0.5, 1.1),
 ncol=1,
 fancybox=True,
 shadow=True,
 )
fig.text(0.5, 0.04, "data", ha="center", va="center")
fig.text(0.06, 0.5, "target", ha="center", va="center", rotation="vertical")
fig.suptitle("Support Vector Regression", fontsize=14)
plt.show ()