聚类与 PCA：没有标签时如何观察数据结构

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

scaled = StandardScaler().fit_transform(X)
pca = PCA().fit(scaled)
print("explained:", pca.explained_variance_ratio_)
print("cumulative:", pca.explained_variance_ratio_.cumsum())
print("components shape:", pca.components_.shape)

from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
from sklearn.decomposition import PCA
from sklearn.metrics import silhouette_score
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

X, _ = make_blobs(
    n_samples=500, centers=3, n_features=5,
    cluster_std=1.2, random_state=42,
)

for cluster_count in (2, 3, 4):
    pipeline = make_pipeline(
        StandardScaler(),
        KMeans(n_clusters=cluster_count, n_init=10, random_state=42),
    )
    labels = pipeline.fit_predict(X)
    scaled = pipeline.named_steps["standardscaler"].transform(X)
    print(cluster_count, round(silhouette_score(scaled, labels), 3))

scaled = StandardScaler().fit_transform(X)
projected = PCA(n_components=2, random_state=42).fit_transform(scaled)
print("projected shape:", projected.shape)

import pandas as pd

clusterer = make_pipeline(
    StandardScaler(),
    KMeans(n_clusters=3, n_init=10, random_state=42),
)
cluster_labels = clusterer.fit_predict(X)
profile = pd.DataFrame(X, columns=[f"feature_{i}" for i in range(X.shape[1])])
profile["cluster"] = cluster_labels
print(profile.groupby("cluster").agg(["count", "mean", "median"]).round(2))

from sklearn.metrics import adjusted_rand_score

reference = KMeans(n_clusters=3, n_init=10, random_state=1).fit_predict(scaled)
for seed in (2, 3, 4, 5):
    candidate = KMeans(n_clusters=3, n_init=10, random_state=seed).fit_predict(scaled)
    print(seed, round(adjusted_rand_score(reference, candidate), 3))

import matplotlib.pyplot as plt

pca_2d = PCA(n_components=2)
projected = pca_2d.fit_transform(scaled)
figure, axis = plt.subplots(figsize=(6, 4))
axis.scatter(projected[:, 0], projected[:, 1], c=cluster_labels, s=16, alpha=0.7)
axis.set_title(
    f"PCA projection, retained={pca_2d.explained_variance_ratio_.sum():.1%}"
)
axis.set_xlabel("PC1")
axis.set_ylabel("PC2")
figure.tight_layout()
figure.savefig("cluster_projection.png", dpi=150)
plt.close(figure)