تحليل المكونات الرئيسية وتخفيض الأبعاد

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
import numpy as np
import matplotlib.pyplot as plt

class="tok-comment"># ── Sample data ────────────────────────────────────────────────────────
X_raw, y = make_classification(n_samples=class="tok-num">400, n_features=class="tok-num">20,
                                n_informative=class="tok-num">8, random_state=class="tok-num">42)
X_train, X_test, _, _ = train_test_split(X_raw, y, test_size=class="tok-num">0.2, random_state=class="tok-num">42)

class="tok-comment"># ── Fit PCA ────────────────────────────────────────────────────────
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X_train)

class="tok-comment"># Fit full PCA first to inspect variance
pca_full = PCA().fit(X_scaled)
cumvar = np.cumsum(pca_full.explained_variance_ratio_)
k = np.argmax(cumvar >= class="tok-num">0.95) + class="tok-num">1
print(fclass="tok-str">"{k} components explain ≥class="tok-num">95% variance")

class="tok-comment"># Final PCA with chosen k
pca = PCA(n_components=k, random_state=class="tok-num">42)
X_pca = pca.fit_transform(X_scaled)          class="tok-comment"># fit on train only
X_test_pca = pca.transform(scaler.transform(X_test))

class="tok-comment"># ── Reconstruction error ───────────────────────────────────────────
X_reconstructed = pca.inverse_transform(X_pca)
recon_err = np.mean((X_scaled - X_reconstructed)**class="tok-num">2)
print(fclass="tok-str">"Reconstruction MSE: {recon_err:.4f}")

class="tok-comment"># ── 2D visualisation ───────────────────────────────────────────────
pca2 = PCA(n_components=class="tok-num">2)
X_2d = pca2.fit_transform(X_scaled)
plt.scatter(X_2d[:,class="tok-num">0], X_2d[:,class="tok-num">1], c=y, cmap=class="tok-str">'viridis', alpha=class="tok-num">0.7)
plt.xlabel(fclass="tok-str">"PC1 ({pca2.explained_variance_ratio_[class="tok-num">0]:.class="tok-num">1%})")
plt.ylabel(fclass="tok-str">"PC2 ({pca2.explained_variance_ratio_[class="tok-num">1]:.class="tok-num">1%})")