聚类算法之简介

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

# 1. 生成聚类数据
print("=== 1. 生成聚类数据 ===")
X, y_true = make_blobs(
    n_samples=300,
    centers=4,
    cluster_std=0.60,
    random_state=42
)

print(f"数据形状: {X.shape}")
print(f"真实类别数: {len(np.unique(y_true))}")

# 2. 距离计算示例
print("\n=== 2. 距离计算示例 ===")

point1 = np.array([1, 2])
point2 = np.array([4, 6])

# 欧式距离
euclidean_dist = np.sqrt(np.sum((point1 - point2) ** 2))
print(f"欧式距离: {euclidean_dist:.4f}")

# 曼哈顿距离
manhattan_dist = np.sum(np.abs(point1 - point2))
print(f"曼哈顿距离: {manhattan_dist:.4f}")

# 切比雪夫距离
chebyshev_dist = np.max(np.abs(point1 - point2))
print(f"切比雪夫距离: {chebyshev_dist:.4f}")

# 米氏距离（p=3）
minkowski_dist = np.sum(np.abs(point1 - point2) ** 3) ** (1/3)
print(f"米氏距离(p=3): {minkowski_dist:.4f}")

# 3. KMeans聚类
print("\n=== 3. KMeans聚类 ===")
kmeans = KMeans(
    n_clusters=4,
    random_state=42,
    n_init=10
)
kmeans.fit(X)

# 预测
y_pred = kmeans.predict(X)
print(f"预测类别数: {len(np.unique(y_pred))}")

# 聚类中心
centers = kmeans.cluster_centers_
print(f"聚类中心形状: {centers.shape}")
print(f"聚类中心:\n{centers}")

# 4. 可视化
print("\n=== 4. 可视化 ===")
plt.figure(figsize=(12, 5))

# 原始数据
plt.subplot(1, 2, 1)
plt.scatter(X[:, 0], X[:, 1], c=y_true, cmap='viridis')
plt.title('原始数据（真实标签）')

# 聚类结果
plt.subplot(1, 2, 2)
plt.scatter(X[:, 0], X[:, 1], c=y_pred, cmap='viridis')
plt.scatter(centers[:, 0], centers[:, 1], c='red', marker='x', s=200, linewidths=3)
plt.title('KMeans聚类结果')

plt.tight_layout()
plt.savefig('kmeans_clustering.png', dpi=100)
print("聚类结果图已保存")

# 5. 顾客数据分群模拟
print("\n=== 5. 顾客数据分群模拟 ===")
np.random.seed(42)

# 模拟顾客数据：年收入和支出
n_customers = 300

# 5个群体
group1 = np.random.randn(60, 2) * 10 + [20, 20]    # 赚少花少
group2 = np.random.randn(60, 2) * 10 + [20, 80]    # 赚少花多（年轻人）
group3 = np.random.randn(60, 2) * 10 + [50, 50]    # 正常
group4 = np.random.randn(60, 2) * 10 + [80, 20]    # 赚多花少
group5 = np.random.randn(60, 2) * 10 + [80, 80]    # 赚多花多

customer_data = np.vstack([group1, group2, group3, group4, group5])

print(f"顾客数据形状: {customer_data.shape}")
print(f"年收入范围: {customer_data[:, 0].min():.2f} - {customer_data[:, 0].max():.2f}")
print(f"支出范围: {customer_data[:, 1].min():.2f} - {customer_data[:, 1].max():.2f}")

# KMeans聚类
kmeans_customer = KMeans(n_clusters=5, random_state=42, n_init=10)
customer_labels = kmeans_customer.fit_predict(customer_data)

# 可视化
plt.figure(figsize=(10, 8))
scatter = plt.scatter(
    customer_data[:, 0], customer_data[:, 1],
    c=customer_labels, cmap='viridis', alpha=0.6
)
plt.scatter(
    kmeans_customer.cluster_centers_[:, 0],
    kmeans_customer.cluster_centers_[:, 1],
    c='red', marker='x', s=200, linewidths=3
)
plt.xlabel('年收入（万元）')
plt.ylabel('支出（万元）')
plt.title('顾客数据分群')
plt.colorbar(scatter)
plt.savefig('customer_clustering.png', dpi=100)
print("顾客分群图已保存")

# 6. 不同K值的效果
print("\n=== 6. 不同K值的效果 ===")
fig, axes = plt.subplots(2, 3, figsize=(15, 10))

for idx, k in enumerate([2, 3, 4, 5, 6, 7]):
    ax = axes[idx // 3, idx % 3]
    
    kmeans = KMeans(n_clusters=k, random_state=42, n_init=10)
    labels = kmeans.fit_predict(X)
    
    ax.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
    ax.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1],
               c='red', marker='x', s=100)
    ax.set_title(f'K={k}')

plt.tight_layout()
plt.savefig('different_k_values.png', dpi=100)
print("不同K值效果图已保存")

# 7. 相似度计算函数
print("\n=== 7. 相似度计算函数 ===")

def calculate_similarity(point1, point2, method='euclidean'):
    """计算两个点的相似度（距离）"""
    point1 = np.array(point1)
    point2 = np.array(point2)
    
    if method == 'euclidean':
        # 欧式距离
        return np.sqrt(np.sum((point1 - point2) ** 2))
    elif method == 'manhattan':
        # 曼哈顿距离
        return np.sum(np.abs(point1 - point2))
    elif method == 'chebyshev':
        # 切比雪夫距离
        return np.max(np.abs(point1 - point2))
    elif method == 'minkowski':
        # 米氏距离（p=3）
        p = 3
        return np.sum(np.abs(point1 - point2) ** p) ** (1/p)
    else:
        raise ValueError(f"未知距离度量: {method}")

# 测试
p1 = [1, 2]
p2 = [4, 6]

for method in ['euclidean', 'manhattan', 'chebyshev', 'minkowski']:
    dist = calculate_similarity(p1, p2, method)
    print(f"{method}: {dist:.4f}")