Lecture 6 ¶

import statsmodels.api as sm
import numpy as np

X = sm.add_constant(X)  # 添加截距项
model = sm.OLS(y, X).fit()

# 获取 Cook's Distance
influence = model.get_influence()
cooks_d = influence.cooks_distance[0]

# 标记影响点
influential = np.where(cooks_d > 4 / len(X))[0]
print(f"影响点索引: {influential}")
print(f"对应 Cook's D: {cooks_d[influential]}")

import pandas as pd

# 假设 color 列有 red, green, blue 三个类别
df_encoded = pd.get_dummies(df, columns=['color'], drop_first=True)
# drop_first=True 删除第一个类别，避免完全共线性
# 结果：color_green, color_blue（red 作为基准类别）

import statsmodels.api as sm
import matplotlib.pyplot as plt

# LOWESS 平滑
lowess_result = sm.nonparametric.lowess(y, x, frac=0.3)  # frac 控制平滑程度

plt.scatter(x, y, alpha=0.5, label='原始数据')
plt.plot(lowess_result[:, 0], lowess_result[:, 1],
         color='red', linewidth=2, label='LOWESS')
plt.legend()
plt.show()

from sklearn.neighbors import KNeighborsClassifier
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline

# KNN 需要特征缩放
pipeline = Pipeline([
    ('scaler', StandardScaler()),
    ('knn', KNeighborsClassifier(n_neighbors=5))
])
pipeline.fit(X_train, y_train)
y_pred = pipeline.predict(X_test)

from sklearn.tree import DecisionTreeClassifier, export_text

# 训练决策树
dt = DecisionTreeClassifier(max_depth=3, min_samples_split=10, random_state=42)
dt.fit(X_train, y_train)

# 查看决策规则
print(export_text(dt, feature_names=list(X.columns)))

from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

# 标准化
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# 训练 K-Means
kmeans = KMeans(n_clusters=3, random_state=42, n_init=10)
kmeans.fit(X_scaled)

# 结果
print(f"簇中心:\n{kmeans.cluster_centers_}")
print(f"Inertia (SSE): {kmeans.inertia_:.2f}")
print(f"标签: {kmeans.labels_}")

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

Z = linkage(X_scaled, method='ward')  # Ward 方差最小化
plt.figure(figsize=(12, 6))
dendrogram(Z, truncate_mode='level', p=5)
plt.title('Hierarchical Clustering Dendrogram')
plt.xlabel('Sample Index')
plt.ylabel('Distance')
plt.show()

from sklearn.cluster import DBSCAN

dbscan = DBSCAN(eps=0.5, min_samples=5)
labels = dbscan.fit_predict(X_scaled)

n_clusters = len(set(labels)) - (1 if -1 in labels else 0)
n_noise = list(labels).count(-1)
print(f"簇数: {n_clusters}, 噪声点: {n_noise}")

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

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

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

plt.scatter(X_pca[:, 0], X_pca[:, 1], c=y, cmap='viridis', alpha=0.6)
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.title('PCA Projection')
plt.colorbar()
plt.show()