无监督学习：聚类与降维

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

# 生成 3 个簇的示例数据
X, y_true = make_blobs(n_samples=400, centers=3, cluster_std=0.8, random_state=42)
X = StandardScaler().fit_transform(X)  # K-Means 依赖距离，必须标准化

kmeans = KMeans(n_clusters=3, n_init=10, random_state=42)
labels = kmeans.fit_predict(X)

# 可视化
plt.scatter(X[:,0], X[:,1], c=labels, cmap="viridis", alpha=0.6)
plt.scatter(kmeans.cluster_centers_[:,0], kmeans.cluster_centers_[:,1],
            marker="X", s=200, c="red", label="质心")
plt.legend()
plt.title("K-Means 聚类结果")
plt.savefig("kmeans.png", dpi=120)

inertias = []  # 簇内平方和（SSE），越小越好，但 K 越大 SSE 越小
for k in range(1, 11):
    km = KMeans(n_clusters=k, n_init=10, random_state=42)
    km.fit(X)
    inertias.append(km.inertia_)

plt.plot(range(1, 11), inertias, "bo-")
plt.xlabel("K（簇数量）")
plt.ylabel("SSE（簇内平方和）")
plt.title("肘部法则：曲线弯折处是最优 K")
plt.savefig("elbow.png", dpi=120)

from sklearn.cluster import DBSCAN
from sklearn.datasets import make_moons

X_moon, _ = make_moons(n_samples=300, noise=0.05, random_state=42)

# eps：邻域半径；min_samples：核心点至少有多少邻居
dbscan = DBSCAN(eps=0.2, min_samples=5)
labels = dbscan.fit_predict(X_moon)

# label=-1 表示噪声点
n_clusters = len(set(labels)) - (1 if -1 in labels else 0)
n_noise    = (labels == -1).sum()
print(f"发现 {n_clusters} 个簇，{n_noise} 个噪声点")

from sklearn.metrics import silhouette_score, davies_bouldin_score

# 轮廓系数：-1~1，越接近 1 表示簇内紧、簇间散
sil = silhouette_score(X, labels)
print(f"轮廓系数: {sil:.3f}")

# Davies-Bouldin 指数：越小越好
db = davies_bouldin_score(X, labels)
print(f"Davies-Bouldin: {db:.3f}")

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

X, y = load_digits(return_X_y=True)  # 64 维手写数字图像
print(f"原始维度: {X.shape}")  # (1797, 64)

pca = PCA(n_components=2)
X_2d = pca.fit_transform(X)
print(f"降维后:   {X_2d.shape}")  # (1797, 2)

# 可视化（二维散点图）
plt.figure(figsize=(10, 8))
scatter = plt.scatter(X_2d[:,0], X_2d[:,1], c=y, cmap="tab10", alpha=0.6, s=15)
plt.colorbar(scatter)
plt.title("PCA 将 64 维降至 2 维")
plt.savefig("pca_digits.png", dpi=120)

pca_full = PCA().fit(X)
cumvar = np.cumsum(pca_full.explained_variance_ratio_)

plt.plot(cumvar)
plt.axhline(0.95, color="r", linestyle="--", label="95% 方差")
plt.xlabel("主成分数量")
plt.ylabel("累计解释方差比")
plt.legend()

# 找到解释 95% 方差所需的最少主成分数
n_components_95 = np.argmax(cumvar >= 0.95) + 1
print(f"解释 95% 方差需要 {n_components_95} 个主成分")

from sklearn.manifold import TSNE

# 注意：t-SNE 很慢，大数据集先用 PCA 降到 50 维再跑 t-SNE
X_50d = PCA(n_components=50).fit_transform(X)

tsne = TSNE(n_components=2, perplexity=30, random_state=42, n_iter=1000)
X_tsne = tsne.fit_transform(X_50d)

plt.figure(figsize=(10, 8))
scatter = plt.scatter(X_tsne[:,0], X_tsne[:,1], c=y, cmap="tab10", s=15, alpha=0.7)
plt.colorbar(scatter)
plt.title("t-SNE 可视化手写数字（每个颜色是一个数字 0-9）")
plt.savefig("tsne_digits.png", dpi=120)

import umap

reducer = umap.UMAP(n_components=2, n_neighbors=15, min_dist=0.1, random_state=42)
X_umap = reducer.fit_transform(X)

from sklearn.ensemble import IsolationForest
import numpy as np

# 生成含异常点的数据
np.random.seed(42)
X_normal  = np.random.randn(300, 2)
X_outlier = np.random.uniform(-4, 4, (20, 2))  # 20 个随机异常点
X_all = np.vstack([X_normal, X_outlier])

iso = IsolationForest(contamination=0.05, random_state=42)  # contamination=异常比例
labels = iso.fit_predict(X_all)  # -1=异常，1=正常

print(f"检测到 {(labels == -1).sum()} 个异常点")

# 查看异常分数（越负越异常）
scores = iso.score_samples(X_all)

from sklearn.neighbors import LocalOutlierFactor

lof = LocalOutlierFactor(n_neighbors=20, contamination=0.05)
labels = lof.fit_predict(X_all)  # -1=异常，1=正常
print(f"LOF 检测到 {(labels == -1).sum()} 个异常点")