def test_hypersphere_kmedoids_fit(self):
gs.random.seed(55)
manifold = hypersphere.Hypersphere(2)
metric = hypersphere.HypersphereMetric(2)
data = manifold.random_von_mises_fisher(kappa=100, n_samples=200)
kmedoids = RiemannianKMedoids(metric=metric, n_clusters=1)
center = kmedoids.fit(data)
self.assertTrue(manifold.belongs(center))
def kmedoids_poincare_ball():
"""Run K-medoids on the Poincare ball."""
n_samples = 20
dim = 2
n_clusters = 2
manifold = PoincareBall(dim=dim)
metric = manifold.metric
cluster_1 = gs.random.uniform(low=0.5, high=0.6, size=(n_samples, dim))
cluster_2 = gs.random.uniform(low=-0.2, high=0, size=(n_samples, dim))
data = gs.concatenate((cluster_1, cluster_2), axis=0)
kmedoids = RiemannianKMedoids(metric=metric, n_clusters=n_clusters, init="random")
centroids = kmedoids.fit(data=data, max_iter=100)
labels = kmedoids.predict(data=data)
plt.figure(1)
colors = ["red", "blue"]
ax = visualization.plot(
data,
space="H2_poincare_disk",
marker=".",
color="black",
point_type=manifold.point_type,
)
for i in range(n_clusters):
ax = visualization.plot(
data[labels == i],
ax=ax,
space="H2_poincare_disk",
marker=".",
color=colors[i],
point_type=manifold.point_type,
)
ax = visualization.plot(
centroids,
ax=ax,
space="H2_poincare_disk",
marker="*",
color="green",
s=100,
point_type=manifold.point_type,
)
ax.set_title("Kmedoids on Poincaré Ball Manifold")
return plt
def test_hypersphere_kmedoids_predict(self):
gs.random.seed(1234)
dim = 2
manifold = hypersphere.Hypersphere(dim)
metric = hypersphere.HypersphereMetric(dim)
data = manifold.random_von_mises_fisher(kappa=100, n_samples=200)
kmedoids = RiemannianKMedoids(metric, n_clusters=5)
centroids = kmedoids.fit(data, max_iter=100)
result = kmedoids.predict(data)
expected = gs.array([
int(metric.closest_neighbor_index(x_i, centroids)) for x_i in data
])
self.assertAllClose(expected, result)
def kmedoids_hypersphere():
"""Run K-medoids on the sphere."""
n_samples = 50
dim = 2
n_clusters = 2
manifold = Hypersphere(dim)
metric = manifold.metric
# Generate data on north pole
cluster_1 = manifold.random_von_mises_fisher(kappa=50, n_samples=n_samples)
# Generate data on south pole
cluster_2 = manifold.random_von_mises_fisher(kappa=50, n_samples=n_samples)
for point in cluster_2:
point[2] = -point[2]
data = gs.concatenate((cluster_1, cluster_2), axis=0)
kmedoids = RiemannianKMedoids(metric=metric, n_clusters=n_clusters)
centroids = kmedoids.fit(data)
labels = kmedoids.predict(data)
plt.figure(2)
colors = ['red', 'blue']
ax = visualization.plot(data, space='S2', marker='.', color='black')
for i in range(n_clusters):
if len(data[labels == i]) > 0:
ax = visualization.plot(points=data[labels == i],
ax=ax,
space='S2',
marker='.',
color=colors[i])
ax = visualization.plot(centroids,
ax=ax,
space='S2',
marker='*',
s=200,
color='green')
ax.set_title('Kmedoids on Hypersphere Manifold')
return plt
def main():
"""Learning Poincaré graph embedding.
Learns Poincaré Ball embedding by using Riemannian
gradient descent algorithm. Then K-means is applied
to learn labels of each data sample.
"""
gs.random.seed(1234)
karate_graph = load_karate_graph()
hyperbolic_embedding = HyperbolicEmbedding()
embeddings = hyperbolic_embedding.embed(karate_graph)
colors = {1: 'b', 2: 'r'}
group_1 = mpatches.Patch(color=colors[1], label='Group 1')
group_2 = mpatches.Patch(color=colors[2], label='Group 2')
circle = visualization.PoincareDisk(point_type='ball')
_, ax = plt.subplots(figsize=(8, 8))
ax.axes.xaxis.set_visible(False)
ax.axes.yaxis.set_visible(False)
circle.set_ax(ax)
circle.draw(ax=ax)
for i_embedding, embedding in enumerate(embeddings):
x_coords = embedding[0]
y_coords = embedding[1]
pt_id = i_embedding
plt.scatter(
x_coords, y_coords,
c=colors[karate_graph.labels[pt_id][0]],
s=150
)
ax.annotate(pt_id, (x_coords, y_coords))
plt.tick_params(
which='both')
plt.title('Poincare Ball Embedding of the Karate Club Network')
plt.legend(handles=[group_1, group_2])
plt.show()
n_clusters = 2
kmeans = RiemannianKMeans(
metric=hyperbolic_embedding.manifold.metric,
n_clusters=n_clusters,
init='random',
mean_method='frechet-poincare-ball')
centroids = kmeans.fit(X=embeddings, max_iter=100)
labels = kmeans.predict(X=embeddings)
colors = ['g', 'c', 'm']
circle = visualization.PoincareDisk(point_type='ball')
_, ax2 = plt.subplots(figsize=(8, 8))
circle.set_ax(ax2)
circle.draw(ax=ax2)
ax2.axes.xaxis.set_visible(False)
ax2.axes.yaxis.set_visible(False)
group_1_predicted = mpatches.Patch(
color=colors[0], label='Predicted Group 1')
group_2_predicted = mpatches.Patch(
color=colors[1], label='Predicted Group 2')
group_centroids = mpatches.Patch(
color=colors[2], label='Cluster centroids')
for _ in range(n_clusters):
for i_embedding, embedding in enumerate(embeddings):
x_coords = embedding[0]
y_coords = embedding[1]
pt_id = i_embedding
if labels[i_embedding] == 0:
color = colors[0]
else:
color = colors[1]
plt.scatter(
x_coords, y_coords,
c=color,
s=150
)
ax2.annotate(pt_id, (x_coords, y_coords))
for _, centroid in enumerate(centroids):
x_coords = centroid[0]
y_coords = centroid[1]
plt.scatter(
x_coords, y_coords,
c=colors[2],
marker='*',
s=150,
)
plt.title('K-means applied to Karate club embedding')
plt.legend(handles=[group_1_predicted, group_2_predicted, group_centroids])
plt.show()
kmedoid = RiemannianKMedoids(
metric=hyperbolic_embedding.manifold.metric,
n_clusters=n_clusters,
init='random')
centroids = kmedoid.fit(data=embeddings, max_iter=100)
labels = kmedoid.predict(data=embeddings)
colors = ['g', 'c', 'm']
circle = visualization.PoincareDisk(point_type='ball')
_, ax2 = plt.subplots(figsize=(8, 8))
circle.set_ax(ax2)
circle.draw(ax=ax2)
ax2.axes.xaxis.set_visible(False)
ax2.axes.yaxis.set_visible(False)
group_1_predicted = mpatches.Patch(
color=colors[0], label='Predicted Group 1')
group_2_predicted = mpatches.Patch(
color=colors[1], label='Predicted Group 2')
group_centroids = mpatches.Patch(
color=colors[2], label='Cluster centroids')
for _ in range(n_clusters):
for i_embedding, embedding in enumerate(embeddings):
x_coords = embedding[0]
y_coords = embedding[1]
pt_id = i_embedding
if labels[i_embedding] == 0:
color = colors[0]
else:
color = colors[1]
plt.scatter(
x_coords, y_coords,
c=color,
s=150
)
ax2.annotate(pt_id, (x_coords, y_coords))
for _, centroid in enumerate(centroids):
x_coords = centroid[0]
y_coords = centroid[1]
plt.scatter(
x_coords, y_coords,
c=colors[2],
marker='*',
s=150,
)
plt.title('K-Medoids applied to Karate club embedding')
plt.legend(handles=[group_1_predicted, group_2_predicted, group_centroids])
plt.show()