Python聚类分析：从数据到可视化

Python 数据可视化之聚类图

聚类图（Cluster Plot）是数据分析和机器学习中常用的可视化工具，用于展示数据的分组结构。Python 提供了多种库（如 scikit-learn、seaborn、matplotlib）来实现聚类分析及可视化。

数据准备与预处理

聚类分析通常需要标准化或归一化数据，以避免量纲差异对聚类结果的影响。使用 sklearn.preprocessing 的 StandardScaler 或 MinMaxScaler 对数据进行预处理。

from sklearn.preprocessing import StandardScaler
import pandas as pd

data = pd.read_csv('data.csv')
scaler = StandardScaler()
scaled_data = scaler.fit_transform(data)

聚类算法选择与训练

常见的聚类算法包括 K-Means、层次聚类（Hierarchical Clustering）和 DBSCAN。以 K-Means 为例，使用 sklearn.cluster 进行训练并获取聚类标签。

from sklearn.cluster import KMeans

kmeans = KMeans(n_clusters=3, random_state=42)
clusters = kmeans.fit_predict(scaled_data)
data['Cluster'] = clusters  # 将聚类结果加入原始数据

可视化聚类结果

1. 散点图展示聚类分布
使用 matplotlib 或 seaborn 绘制散点图，不同颜色代表不同簇。

import matplotlib.pyplot as plt
import seaborn as sns

sns.scatterplot(data=data, x='Feature1', y='Feature2', hue='Cluster', palette='viridis')
plt.title('K-Means Clustering')
plt.show()

2. 层次聚类热图（Dendrogram）
层次聚类可通过树状图展示数据点之间的层次关系。

from scipy.cluster.hierarchy import dendrogram, linkage
import numpy as np

linked = linkage(scaled_data, method='ward')
plt.figure(figsize=(10, 6))
dendrogram(linked, orientation='top', labels=np.arange(len(data)))
plt.title('Hierarchical Clustering Dendrogram')
plt.show()

3. 高维数据降维可视化
对于高维数据，可使用 PCA 或 t-SNE 降维后绘图。

from sklearn.decomposition import PCA

pca = PCA(n_components=2)
pca_result = pca.fit_transform(scaled_data)
data['PCA1'] = pca_result[:, 0]
data['PCA2'] = pca_result[:, 1]

sns.scatterplot(data=data, x='PCA1', y='PCA2', hue='Cluster', palette='Set1')
plt.title('PCA Reduced Clusters')
plt.show()

聚类评估

通过轮廓系数（Silhouette Score）或 Calinski-Harabasz 指数评估聚类质量。

from sklearn.metrics import silhouette_score

score = silhouette_score(scaled_data, clusters)
print(f'Silhouette Score: {score:.2f}')

优化与调参

通过肘部法则（Elbow Method）选择最佳聚类数 K。

inertia = []
for k in range(1, 10):
    kmeans = KMeans(n_clusters=k, random_state=42)
    kmeans.fit(scaled_data)
    inertia.append(kmeans.inertia_)

plt.plot(range(1, 10), inertia, marker='o')
plt.xlabel('Number of Clusters')
plt.ylabel('Inertia')
plt.title('Elbow Method')
plt.show()

总结

Python 提供了强大的工具链实现聚类分析与可视化，涵盖数据预处理、算法选择、结果展示及评估。通过合理调整参数和选择合适的可视化方法，可以清晰呈现数据的内在结构。

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