K-Means 质心在 3D 聚类图中不可见

Question

当我使用此代码在 2D 中绘制聚类结果时：

from matplotlib import pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans

# create 2d data 
x, label = make_blobs(n_samples=3000, n_features=2, centers=4,
                      cluster_std=3, random_state=42)

# cluster data
kmeans = KMeans(init="k-means++", n_clusters=4, random_state=42)
kmeans.fit(x)

# plot clusters and centroids
fig = plt.figure(figsize=(10,5))
ax = fig.add_subplot(111)
ax.scatter(x[:,0],x[:,1], c=kmeans.labels_, cmap='viridis',
           edgecolor='k', s=40, alpha = 0.5)
ax.scatter(kmeans.cluster_centers_[:,0], kmeans.cluster_centers_[:,1],
           s = 300, c = 'r', marker='*', label = 'Centroid')
ax.set_title("2D Kmeans clustering")
ax.set_xlabel("X")
ax.set_ylabel("Y")   
plt.show()

我得到以下输出：

但是当我尝试使用此代码在 3D 中绘制聚类结果时：

from matplotlib import pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans

# create 3d data 
x, label = make_blobs(n_samples=3000, n_features=3, centers=4,
                      cluster_std=3, random_state=42)

# cluster data
kmeans = KMeans(init="k-means++", n_clusters=4, random_state=42)
kmeans.fit(x)

# plot clusters and centroids
fig = plt.figure(figsize=(10,5))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x[:,0], x[:,1], x[:,2] ,c=kmeans.labels_, cmap='viridis',
           edgecolor='k', s=40, alpha = 0.5)
ax.scatter(kmeans.cluster_centers_[:,0], kmeans.cluster_centers_[:,1],
           kmeans.cluster_centers_[:,2], s = 300, c = 'r',
           marker='*', label = 'Centroid')
ax.set_title("3D Kmeans clustering")
ax.set_xlabel("X")
ax.set_ylabel("Y")   
ax.set_zlabel("Z") 
plt.show()

我得到以下输出：

如您所见，每个集群的质心不可见。我想在 3d 图中看到质心星星，我该如何实现？

提前感谢您的帮助！

Answer 1

质心星被点云包围，因此不容易看到。您可以通过使点更小（s=10 或更小）和更透明（alpha=0.1 或更小）来使它们更明显，如以下代码行所示：

ax.scatter(x[:,0], x[:,1], x[:,2] ,c=kmeans.labels_, cmap='viridis',
       edgecolor='k', s=10, alpha = 0.1)