def test_kmeanspp_initialization():
random_state = check_random_state(1)
n_samples = 300
n_features = 2
X = np.ndarray((n_samples, n_features))
X[:n_samples // 3, :] = random_state.multivariate_normal(
[0.0, 1.0], [[0.5, -1.0], [-1.0, 5.0]], size=(n_samples // 3, ))
X[n_samples // 3:-n_samples // 3, :] = random_state.multivariate_normal(
[-2.0, -2.0], [[3.0, 1.0], [1.0, 1.0]], size=(n_samples // 3, ))
X[-n_samples // 3:, :] = random_state.multivariate_normal(
[3.0, 1.0], [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples // 3, ))
# artificial scaling, makes standard implementation fail
# either the initial covariances have to be adjusted or we have
# to normalize the dataset
X[:, 1] *= 10000.0
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="random")
ellipses = gmm.to_ellipses()
widths = np.array([ellipsis_params[1]
for _, ellipsis_params in ellipses])[:, np.newaxis]
average_widths_random = np.mean(pdist(widths))
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="kmeans++")
ellipses = gmm.to_ellipses()
widths = np.array([ellipsis_params[1]
for _, ellipsis_params in ellipses])[:, np.newaxis]
average_widths_kmeanspp = np.mean(pdist(widths))
# random initialization produces uneven covariance scaling
assert_less(average_widths_kmeanspp, average_widths_random)
def test_ellipses():
"""Test equiprobable ellipses."""
random_state = check_random_state(0)
means = np.array([[0.0, 1.0], [2.0, -1.0]])
covariances = np.array([[[0.5, 0.0], [0.0, 5.0]], [[5.0, 0.0], [0.0,
0.5]]])
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=random_state)
ellipses = gmm.to_ellipses()
mean, (angle, width, height) = ellipses[0]
assert_array_almost_equal(means[0], mean)
assert_equal(angle, 0.5 * np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
mean, (angle, width, height) = ellipses[1]
assert_array_almost_equal(means[1], mean)
assert_equal(angle, -np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
def test_ellipses():
"""Test equiprobable ellipses."""
random_state = check_random_state(0)
means = np.array([[0.0, 1.0],
[2.0, -1.0]])
covariances = np.array([[[0.5, 0.0], [0.0, 5.0]],
[[5.0, 0.0], [0.0, 0.5]]])
gmm = GMM(n_components=2, priors=np.array([0.5, 0.5]), means=means,
covariances=covariances, random_state=random_state)
ellipses = gmm.to_ellipses()
mean, (angle, width, height) = ellipses[0]
assert_array_almost_equal(means[0], mean)
assert_equal(angle, 0.5 * np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
mean, (angle, width, height) = ellipses[1]
assert_array_almost_equal(means[1], mean)
assert_equal(angle, -np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
plt.plot(means_over_time[:, 0], means_over_time[:, 1], c="r", lw=2)
plt.fill_between(means_over_time[:, 0],
means_over_time[:, 1] - 1.96 * y_stds,
means_over_time[:, 1] + 1.96 * y_stds,
color="r",
alpha=0.5)
if plot_covariances:
colors = cycle(["r", "g", "b"])
for factor in np.linspace(0.5, 4.0, 8):
new_gmm = GMM(n_components=len(gmm.means),
priors=gmm.priors,
means=gmm.means[:, 1:],
covariances=gmm.covariances[:, 1:, 1:],
random_state=gmm.random_state)
for mean, (angle, width, height) in new_gmm.to_ellipses(factor):
ell = Ellipse(xy=mean,
width=width,
height=height,
angle=np.degrees(angle))
ell.set_alpha(0.15)
ell.set_color(next(colors))
plt.gca().add_artist(ell)
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
plt.subplot(122)
plt.title("Confidence Interval from Raw Data")
plt.plot(X[:, :, 0].T, X[:, :, 1].T, c="k", alpha=0.1)
