03 - 无监督学习¶

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

# 计算不同K值的损失
losses = []
K_range = range(1, 11)
for k in K_range:
    kmeans = KMeans(n_clusters=k, random_state=42)
    kmeans.fit(X)
    losses.append(kmeans.inertia_)  # 损失函数值

# 绘制肘部图
plt.plot(K_range, losses, 'bo-')
plt.xlabel('K值')
plt.ylabel('损失 (SSE)')
plt.show()

# 找到"肘部" (下降速度明显变缓的点)

from sklearn.cluster import KMeans
import numpy as np

# 示例数据
X = np.array([
    [1, 2], [1, 4], [1, 0],
    [10, 2], [10, 4], [10, 0]
])

# 训练
kmeans = KMeans(
    n_clusters=2,      # 簇的数量
    init='k-means++',  # 初始化方法
    max_iter=300,      # 最大迭代次数
    random_state=42
)
kmeans.fit(X)

# 预测
labels = kmeans.labels_        # 每个样本的簇标签
centers = kmeans.cluster_centers_  # 簇中心

print(f"簇标签: {labels}")
print(f"簇中心:\n{centers}")

# 预测新样本
new_samples = [[1, 1], [10, 3]]
predictions = kmeans.predict(new_samples)
print(f"预测: {predictions}")

from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage
import matplotlib.pyplot as plt

# 凝聚层次聚类
agg = AgglomerativeClustering(
    n_clusters=3,          # 簇的数量
    linkage='ward'         # 链接方式
)
labels = agg.fit_predict(X)

# 绘制层次树
linkage_matrix = linkage(X, method='ward')
plt.figure(figsize=(10, 7))
dendrogram(linkage_matrix)
plt.title('层次聚类树')
plt.xlabel('样本索引')
plt.ylabel('距离')
plt.show()

from sklearn.decomposition import PCA
import matplotlib.pyplot as plt

# 标准化 (重要!)
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# PCA降维
pca = PCA(n_components=2)  # 降到2维
X_pca = pca.fit_transform(X_scaled)

# 查看解释方差
print(f"各主成分解释方差: {pca.explained_variance_ratio_}")
print(f"累计解释方差: {pca.explained_variance_ratio_.cumsum()}")

# 可视化
plt.scatter(X_pca[:, 0], X_pca[:, 1], c=labels)
plt.xlabel(f'主成分1 ({pca.explained_variance_ratio_[0]:.2%})')
plt.ylabel(f'主成分2 ({pca.explained_variance_ratio_[1]:.2%})')
plt.title('PCA降维可视化')
plt.show()

# 选择保留95%方差
pca_95 = PCA(n_components=0.95)
X_pca_95 = pca_95.fit_transform(X_scaled)
print(f"保留95%方差需要 {pca_95.n_components_} 个主成分")

from sklearn.manifold import TSNE

# t-SNE降维到2维
tsne = TSNE(
    n_components=2,      # 只支持2或3维
    perplexity=30,       # 类似"最近邻数量" (5-50)
    n_iter=1000,         # 迭代次数
    random_state=42
)
X_tsne = tsne.fit_transform(X)

# 可视化
plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=labels, cmap='viridis')
plt.colorbar()
plt.title('t-SNE可视化')
plt.show()

from sklearn.mixture import GaussianMixture

# 拟合GMM
gmm = GaussianMixture(
    n_components=3,     # 高斯数量 (簇数)
    covariance_type='full',  # 协方差类型
    max_iter=100,
    random_state=42
)
gmm.fit(X)

# 预测簇标签
labels = gmm.predict(X)

# 预测概率 (软聚类)
proba = gmm.predict_proba(X)
# proba[i, k] = 样本i属于簇k的概率

# 查看参数
means = gmm.means_              # 各高斯的均值
covariances = gmm.covariances_  # 各高斯的协方差
weights = gmm.weights_          # 混合系数

print(f"各高斯权重: {weights}")
print(f"各高斯均值:\n{means}")

from sklearn.metrics import silhouette_score, calinski_harabasz_score

# 轮廓系数 (-1到1,越大越好)
score = silhouette_score(X, labels)

# Calinski-Harabasz指数 (越大越好)
score_ch = calinski_harabasz_score(X, labels)