示例13 持久图向量化做分类

"""ex13_ml_features.py — 第 10 章 持久图向量化做分类

对应教程：tutorials/10-advanced.md、tutorials/05-visualization.md 5.5 节。

把持久图压缩成固定维度特征向量，训练一个简单分类器，
区分「圆环」与「随机点云」两类。展示 TDA → ML 的完整管线。

依赖：scikit-learn（pip install scikit-learn）

运行：
python ex13_ml_features.py
"""

import numpy as np
from ripser import ripser
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import cross_val_score

from common import sample_circle, sample_random, persistence_stats

def build_dataset(n_samples=40, seed=0):
"""构造 (X_features, y_label) 数据集。

每个样本：生成一个点云 → 算持久同调 → 提取统计特征。
标签：1 = 圆环，0 = 随机。
"""
rng = np.random.default_rng(seed)
X, y = [], []
for i in range(n_samples):
    # 随机化点数、噪声，让任务更有挑战
    n_pts = int(rng.integers(60, 120))
    noise = float(rng.uniform(0.03, 0.15))

    # 圆环
    circle = sample_circle(n=n_pts, noise=noise, seed=i)
    dgms = ripser(circle, maxdim=1)['dgms']
    X.append(persistence_stats(dgms))
    y.append(1)

    # 随机
    rand = sample_random(n=n_pts, dim=2, seed=i)
    dgms = ripser(rand, maxdim=1)['dgms']
    X.append(persistence_stats(dgms))
    y.append(0)
return np.array(X), np.array(y)
​

def main():
print("构建数据集（圆环 vs 随机点）...")
X, y = build_dataset(n_samples=40, seed=0)
print(f" X shape={X.shape}, 标签分布: {np.bincount(y)}")
print(f" 特征维度: {X.shape[1]}（每维 4 个统计量：点数/max/mean/std）")

# 看一下两类特征均值差异
print("\n=== 两类特征均值对比 ===")
feat_names = ['H0_count', 'H0_max', 'H0_mean', 'H0_std',
              'H1_count', 'H1_max', 'H1_mean', 'H1_std']
for j, name in enumerate(feat_names):
    print(f"  {name:10s}: 圆环={X[y==1, j].mean():8.3f}  "
          f"随机={X[y==0, j].mean():8.3f}")

# 逻辑回归 + 5 折交叉验证
clf = LogisticRegression(max_iter=1000)
scores = cross_val_score(clf, X, y, cv=5, scoring='accuracy')
print(f"\n=== 逻辑回归 5 折交叉验证 ===")
print(f"  accuracy: {scores.mean():.3f} ± {scores.std():.3f}")
print(f"  各折: {np.round(scores, 3)}")

print("\n解读：H1_max（H1 最大持久性）是最具区分度的特征——")
print("      圆环的 H1 显著点持久性远大于随机点。")
​

if name == "main":
main()