def test_nested_circles():
# Test the linear separability of the first 2D KPCA transform
X, y = make_circles(n_samples=400, factor=.3, noise=.05,
random_state=0)
# 2D nested circles are not linearly separable
train_score = Perceptron().fit(X, y).score(X, y)
assert_less(train_score, 0.8)
# Project the circles data into the first 2 components of a RBF Kernel
# PCA model.
# Note that the gamma value is data dependent. If this test breaks
# and the gamma value has to be updated, the Kernel PCA example will
# have to be updated too.
kpca = KernelPCA(kernel="rbf", n_components=2,
fit_inverse_transform=True, gamma=2.)
X_kpca = kpca.fit_transform(X)
# The data is perfectly linearly separable in that space
train_score = Perceptron().fit(X_kpca, y).score(X_kpca, y)
assert_equal(train_score, 1.0)
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