Python怎样实现数据聚类？K-means算法优化

scikit-learn

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

# 生成一些示例数据
X, _ = make_blobs(n_samples=300, centers=4, cluster_std=0.60, random_state=0)

# 初始化KMeans模型，设定簇的数量为4
# n_init='auto' (或一个整数) 告诉算法运行多少次不同的初始质心，并选择最好的结果，这本身就是一种优化
kmeans = KMeans(n_clusters=4, random_state=0, n_init='auto')

# 拟合数据
kmeans.fit(X)

# 获取聚类结果和簇中心
labels = kmeans.labels_
centroids = kmeans.cluster_centers_

# 可视化结果
plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='viridis')
plt.scatter(centroids[:, 0], centroids[:, 1], c='red', s=200, alpha=0.7, marker='X')
plt.title('K-means Clustering')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.show()

print("簇中心点：\n", centroids)

n_init='auto'

n_init=10

init='k-means++'

inertia_

wcss = []
# 尝试不同的K值
for i in range(1, 11): # 尝试从1到10个簇
    kmeans = KMeans(n_clusters=i, random_state=0, n_init='auto')
    kmeans.fit(X)
    wcss.append(kmeans.inertia_) # inertia_ 就是WCSS

plt.plot(range(1, 11), wcss)
plt.title('Elbow Method')
plt.xlabel('Number of Clusters (K)')
plt.ylabel('WCSS')
plt.show()

from sklearn.metrics import silhouette_score

silhouette_scores = []
# K值至少需要2个簇才能计算轮廓系数
for i in range(2, 11):
    kmeans = KMeans(n_clusters=i, random_state=0, n_init='auto')
    kmeans.fit(X)
    score = silhouette_score(X, kmeans.labels_)
    silhouette_scores.append(score)

plt.plot(range(2, 11), silhouette_scores)
plt.title('Silhouette Score Method')
plt.xlabel('Number of Clusters (K)')
plt.ylabel('Silhouette Score')
plt.show()

# 找到最佳K值
best_k = np.argmax(silhouette_scores) + 2 # 因为我们从K=2开始
print(f"根据轮廓系数法，最佳K值可能是：{best_k}")

n_init

from sklearn.cluster import DBSCAN
from sklearn.preprocessing import StandardScaler

# DBSCAN对特征缩放敏感，通常需要先进行标准化
X_scaled = StandardScaler().fit_transform(X)

# eps: 邻域半径, min_samples: 形成核心点所需的最小样本数
dbscan = DBSCAN(eps=0.3, min_samples=5)
clusters = dbscan.fit_predict(X_scaled)

plt.scatter(X_scaled[:, 0], X_scaled[:, 1], c=clusters, s=50, cmap='viridis')
plt.title('DBSCAN Clustering')
plt.xlabel('Scaled Feature 1')
plt.ylabel('Scaled Feature 2')
plt.show()
print("DBSCAN发现的簇标签：", np.unique(clusters)) # -1表示噪声点

from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage

# 生成一些新的数据，以便更好地展示层次聚类
X_hier, _ = make_blobs(n_samples=50, centers=3, cluster_std=0.8, random_state=42)

# 凝聚层次聚类
# n_clusters=None 表示不预设簇的数量，可以后续通过linkage矩阵和dendrogram来确定
# linkage='ward' 是一种合并策略，尝试最小化合并后簇内方差的增加
agg_cluster = AgglomerativeClustering(n_clusters=3, linkage='ward')
agg_labels = agg_cluster.fit_predict(X_hier)

plt.scatter(X_hier[:, 0], X_hier[:, 1], c=agg_labels, s=50, cmap='viridis')
plt.title('Agglomerative Clustering')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.show()

# 绘制树状图（需要scipy库）
linked = linkage(X_hier, method='ward')
plt.figure(figsize=(10, 7))
dendrogram(linked,
           orientation='top',
           distance_sort='descending',
           show_leaf_counts=True)
plt.title('Dendrogram for Agglomerative Clustering')
plt.xlabel('Sample Index')
plt.ylabel('Distance')
plt.show()

from sklearn.mixture import GaussianMixture

# n_components 对应于簇的数量
gmm = GaussianMixture(n_components=4, random_state=0)
gmm.fit(X)
gmm_labels = gmm.predict(X)

plt.scatter(X[:, 0], X[:, 1], c=gmm_labels, s=50, cmap='viridis')
plt.title('Gaussian Mixture Model Clustering')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.show()

# 还可以获取每个样本属于每个簇的概率
# probabilities = gmm.predict_proba(X)
# print("部分样本属于各簇的概率：\n", probabilities[:5])