def __init__(self, n_meridians=40, n_circles_latitude=None, points=None):
if n_circles_latitude is None:
n_circles_latitude = max(n_meridians / 2, 4)
u, v = gs.meshgrid(gs.arange(0, 2 * gs.pi, 2 * gs.pi / n_meridians),
gs.arange(0, gs.pi, gs.pi / n_circles_latitude))
self.center = gs.zeros(3)
self.radius = 1
self.sphere_x = self.center[0] + self.radius * gs.cos(u) * gs.sin(v)
self.sphere_y = self.center[1] + self.radius * gs.sin(u) * gs.sin(v)
self.sphere_z = self.center[2] + self.radius * gs.cos(v)
self.points = []
if points is not None:
self.add_points(points)
def plot_gaussian_mixture_distribution(
data,
mixture_coefficients,
means,
variances,
plot_precision=DEFAULT_PLOT_PRECISION,
save_path="",
metric=None,
):
"""Plot Gaussian Mixture Model."""
x_axis_samples = gs.linspace(-1, 1, plot_precision)
y_axis_samples = gs.linspace(-1, 1, plot_precision)
x_axis_samples, y_axis_samples = gs.meshgrid(x_axis_samples, y_axis_samples)
z_axis_samples = gs.zeros((plot_precision, plot_precision))
for z_index, _ in enumerate(z_axis_samples):
x_y_plane_mesh = gs.concatenate(
(
gs.expand_dims(x_axis_samples[z_index], -1),
gs.expand_dims(y_axis_samples[z_index], -1),
),
axis=-1,
)
mesh_probabilities = weighted_gmm_pdf(
mixture_coefficients, x_y_plane_mesh, means, variances, metric
)
z_axis_samples[z_index] = mesh_probabilities.sum(-1)
fig = plt.figure(
"Learned Gaussian Mixture Model "
"via Expectation Maximization on Poincaré Disc"
)
ax = fig.gca(projection="3d")
ax.plot_surface(
x_axis_samples,
y_axis_samples,
z_axis_samples,
rstride=1,
cstride=1,
linewidth=1,
antialiased=True,
cmap=plt.get_cmap("viridis"),
)
z_circle = -0.8
p = Circle((0, 0), 1, edgecolor="b", lw=1, facecolor="none")
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=z_circle, zdir="z")
for data_index, _ in enumerate(data):
ax.scatter(
data[data_index][0], data[data_index][1], z_circle, c="b", marker="."
)
for means_index, _ in enumerate(means):
ax.scatter(
means[means_index][0], means[means_index][1], z_circle, c="r", marker="D"
)
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_zlim(-0.8, 0.4)
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("P")
plt.savefig(save_path, format="pdf")
return plt