第 7 章 · 决策树与聚类代码实验¶

# 加载 Wine 经典分类数据集：13 个化学特征预测 3 类葡萄酒。
wine = load_wine(as_frame=True)
tree_df = wine.frame.copy()
feature_names = wine.feature_names
feature_names_cn = [
    "酒精", "苹果酸", "灰分", "灰分碱度", "镁", "总酚", "黄酮",
    "非黄酮酚", "原花青素", "颜色强度", "色调", "稀释酒吸光度", "脯氨酸",
]
feature_cn_map = dict(zip(feature_names, feature_names_cn))
class_names = [f"葡萄酒第 {i} 类" for i in range(len(wine.target_names))]
tree_df["类别名称"] = tree_df["target"].map(dict(enumerate(class_names)))

X_tree = tree_df[feature_names]
y_tree = tree_df["target"]

summary_df = pd.DataFrame(
    {
        "样本数": [len(tree_df)],
        "特征数": [len(feature_names)],
        "类别数": [len(class_names)],
    }
)
display(summary_df)
display(tree_df.rename(columns=feature_cn_map).head(8))
display(tree_df["类别名称"].value_counts().rename_axis("类别").reset_index(name="样本数"))

# 划分训练集和测试集，再训练决策树。
X_train, X_test, y_train, y_test = train_test_split(
    X_tree,
    y_tree,
    test_size=0.28,
    stratify=y_tree,
    random_state=7,
)

tree = DecisionTreeClassifier(max_depth=4, min_samples_leaf=3, random_state=7)
tree.fit(X_train, y_train)

train_pred = tree.predict(X_train)
test_pred = tree.predict(X_test)
score_df = pd.DataFrame(
    [
        {"数据": "训练集", "样本数": len(y_train), "准确率": accuracy_score(y_train, train_pred)},
        {"数据": "测试集", "样本数": len(y_test), "准确率": accuracy_score(y_test, test_pred)},
    ]
).round(3)
display(score_df)

test_result = X_test.rename(columns=feature_cn_map).copy()
test_result["真实类别"] = [class_names[i] for i in y_test]
test_result["预测类别"] = [class_names[i] for i in test_pred]
test_result["预测正确"] = test_result["真实类别"].eq(test_result["预测类别"])
display(test_result.head(12))

# 查看分裂规则、特征重要性和混淆矩阵。
importance_df = pd.DataFrame(
    {"特征": feature_names_cn, "重要性": tree.feature_importances_}
).sort_values("重要性", ascending=False)
importance_df["累计重要性"] = importance_df["重要性"].cumsum()

confusion_df = pd.DataFrame(
    confusion_matrix(y_test, test_pred),
    index=[f"真实_{name}" for name in class_names],
    columns=[f"预测_{name}" for name in class_names],
)

print(export_text(tree, feature_names=feature_names_cn, max_depth=3))
display(importance_df.head(10).round(3))
display(confusion_df)

# 绘制树结构和特征重要性条形图。
fig, ax = plt.subplots(figsize=(12.0, 6.3))
plot_tree(
    tree,
    feature_names=feature_names_cn,
    class_names=class_names,
    filled=True,
    rounded=True,
    impurity=False,
    ax=ax,
)
ax.set_title("决策树分裂路径", loc="left", fontsize=14, fontweight="bold", color="#0f172a")
plt.tight_layout()
plt.show()

top_importance = importance_df.head(8).sort_values("重要性")
fig, ax = plt.subplots(figsize=(8.4, 5.0))
ax.barh(top_importance["特征"], top_importance["重要性"], color="#2563eb")
ax.set_title("特征重要性前 8 项", loc="left", fontsize=14, fontweight="bold", color="#0f172a")
ax.set_xlabel("重要性")
ax.grid(True, axis="x", color="#e2e8f0", linewidth=0.8)
plt.tight_layout()
plt.show()

# 加载 Iris 鸢尾花数据集，用四个形态特征做聚类。
iris = load_iris(as_frame=True)
iris_df = iris.frame.copy()
iris_feature_names = iris.feature_names
iris_feature_names_cn = ["萼片长度", "萼片宽度", "花瓣长度", "花瓣宽度"]
iris_feature_cn_map = dict(zip(iris_feature_names, iris_feature_names_cn))
iris_class_names = list(iris.target_names)
iris_df["品种"] = iris_df["target"].map(dict(enumerate(iris_class_names)))

X_iris = iris_df[iris_feature_names]
scaler = StandardScaler()
X_iris_scaled = scaler.fit_transform(X_iris)
pca = PCA(n_components=2, random_state=0)
iris_pca = pca.fit_transform(X_iris_scaled)

display(iris_df.rename(columns=iris_feature_cn_map).head(8))
display(iris_df["品种"].value_counts().rename_axis("品种").reset_index(name="样本数"))
print("PCA 两个主成分解释方差占比:", np.round(pca.explained_variance_ratio_, 3))

# 比较不同 k：簇内平方和用于肘部曲线，轮廓系数辅助判断聚类分离度。
k_values = range(1, 8)
kmeans_by_k = {}
labels_by_k = {}
metric_rows = []

for k in k_values:
    model = KMeans(n_clusters=k, n_init=20, random_state=4)
    labels = model.fit_predict(X_iris_scaled)
    kmeans_by_k[k] = model
    labels_by_k[k] = labels
    metric_rows.append({
        "k": k,
        "簇内平方和": model.inertia_,
        "轮廓系数": np.nan if k == 1 else silhouette_score(X_iris_scaled, labels),
        "ARI(对照真实品种)": np.nan if k == 1 else adjusted_rand_score(iris.target, labels),
    })

k_metrics = pd.DataFrame(metric_rows).round(3)
k_metrics_display = k_metrics.copy()
for col in ["轮廓系数", "ARI(对照真实品种)"]:
    k_metrics_display[col] = k_metrics_display[col].apply(
        lambda value: "未定义" if pd.isna(value) else f"{value:.3f}"
    )
k_metrics_display["簇内平方和"] = k_metrics_display["簇内平方和"].map(lambda value: f"{value:.3f}")
chosen_k = 3
kmeans = kmeans_by_k[chosen_k]
final_labels = labels_by_k[chosen_k]

clustered_iris = iris_df.copy()
clustered_iris["簇"] = final_labels
cluster_profile = clustered_iris.groupby("簇")[iris_feature_names].mean().rename(columns=iris_feature_cn_map).round(2)
cluster_mix = pd.crosstab(clustered_iris["簇"], clustered_iris["品种"])

display(k_metrics_display)
display(cluster_profile)
display(cluster_mix)

# 在 PCA 平面比较不同 k 的聚类结果。
palette = np.array(["#2563eb", "#f97316", "#16a34a", "#9333ea", "#0f766e", "#be123c", "#64748b"])
fig, axes = plt.subplots(2, 2, figsize=(10.2, 8.0), sharex=True, sharey=True)
for ax, k in zip(axes.ravel(), [2, 3, 4, 5]):
    labels = labels_by_k[k]
    centers_2d = pca.transform(kmeans_by_k[k].cluster_centers_)
    ax.scatter(
        iris_pca[:, 0],
        iris_pca[:, 1],
        c=palette[labels],
        s=58,
        alpha=0.85,
        edgecolors="white",
        linewidth=0.6,
    )
    ax.scatter(
        centers_2d[:, 0],
        centers_2d[:, 1],
        marker="X",
        s=150,
        color="#0f172a",
        edgecolors="white",
        linewidth=0.8,
    )
    ax.set_title(f"k={k}", loc="left", fontweight="bold")
    ax.grid(True, color="#e2e8f0", linewidth=0.8)

fig.suptitle("鸢尾花 KMeans 不同 k 的聚类效果", x=0.08, ha="left", fontsize=14, fontweight="bold", color="#0f172a")
fig.supxlabel("PCA 第一主成分")
fig.supylabel("PCA 第二主成分")
plt.tight_layout()
plt.show()

# 肘部曲线观察簇内平方和下降速度，k=3 后收益明显变小。
fig, ax1 = plt.subplots(figsize=(8.6, 5.0))
ax1.plot(k_metrics["k"], k_metrics["簇内平方和"], marker="o", linewidth=2.4, color="#2563eb", label="簇内平方和")
ax1.axvline(chosen_k, color="#f97316", linestyle="--", linewidth=1.8)
ax1.set_title("肘部曲线与 k 选择", loc="left", fontsize=14, fontweight="bold", color="#0f172a")
ax1.set_xlabel("k")
ax1.set_ylabel("簇内平方和", color="#2563eb")
ax1.tick_params(axis="y", labelcolor="#2563eb")
ax1.grid(True, color="#e2e8f0", linewidth=0.8)

ax2 = ax1.twinx()
ax2.plot(k_metrics["k"], k_metrics["轮廓系数"], marker="s", linewidth=2.0, color="#16a34a", label="轮廓系数")
ax2.set_ylabel("轮廓系数", color="#16a34a")
ax2.tick_params(axis="y", labelcolor="#16a34a")
ax1.text(chosen_k + 0.08, ax1.get_ylim()[1] * 0.82, "选择 k=3", color="#c2410c", fontweight="bold")
plt.tight_layout()
plt.show()