Wiki cleanup: error-doc removal, dedup merge, link normalization

10_Wiki/Topics 대규모 정리: - 오류 캡처/미완성 stub 문서 227개 제거 - 교차폴더 중복 43클러스터 병합 (63파일 → redirect) - 링크명 정규화: 깨진 링크 수정·redirect 직결·개념 매핑 ~2,400건 - 카테고리 MOC 6개 신규 생성 - Graph 섹션 미해결 related-keyword 링크 10,058건 제거 Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-20 23:52:15 +09:00
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 id: wiki-2026-0508-principal-component-analysis
 title: Principal Component Analysis
 category: 10_Wiki/Topics
-status: verified
-canonical_id: self
-aliases: [PCA, Karhunen-Loève Transform, KLT]
-duplicate_of: none
+status: duplicate
+canonical_id: wiki-2026-0508-principle-component-analysis
+duplicate_of: "[[Principal Component Analysis]]"
+aliases: []
 source_trust_level: A
-confidence_score: 0.93
-verification_status: applied
-tags: [linear-algebra, dimensionality-reduction, statistics, ml]
-raw_sources: []
-last_reinforced: 2026-05-10
+confidence_score: 0.9
+verification_status: redirected
+tags: [duplicate]
+last_reinforced: 2026-05-20
 github_commit: pending
-tech_stack:
-  language: python
-  framework: scikit-learn/numpy
 ---

 # Principal Component Analysis

-## 매 한 줄
-> **"매 max-variance orthogonal directions 의 projection"**. Pearson(1901) 의 origin 의 매 covariance eigendecomposition / SVD 의 reduction — 매 visualization, denoising, compression, 매 ML preprocessing 의 baseline.
-
-## 매 핵심
-
-### 매 수학
- 매 centered data X (n×p), 매 covariance C = XᵀX/(n-1).
- 매 eigendecomposition C = VΛVᵀ — 매 V 의 columns 가 principal axes.
- 매 SVD X = UΣVᵀ — 매 numerically stable path; 매 PC scores = UΣ.
- 매 explained variance ratio = λᵢ / Σλⱼ.
-
-### 매 절차
-1. 매 mean-center (and 보통 standardize).
-2. 매 SVD or eigendecomp.
-3. 매 top-k components 의 select (scree / variance threshold).
-4. 매 project: Z = X V_k.
-
-### 매 응용
-1. 시각화 (2D/3D scatter).
-2. Noise filtering / denoising.
-3. Whitening preprocessing.
-4. Compression (face images, MNIST baseline).
-5. Genomics population structure (PC1 vs PC2).
-
-## 💻 패턴
-
-### scikit-learn full pipeline
-```python
-from sklearn.decomposition import PCA
-from sklearn.preprocessing import StandardScaler
-from sklearn.pipeline import make_pipeline
-
-pipe = make_pipeline(StandardScaler(), PCA(n_components=0.95, svd_solver="full"))
-Z = pipe.fit_transform(X)             # explains >=95% variance
-print(pipe[-1].explained_variance_ratio_.cumsum())
-```
-
-### NumPy SVD-based PCA (memory-efficient)
-```python
-import numpy as np
-def pca(X, k):
-    Xc = X - X.mean(axis=0, keepdims=True)
-    U, S, Vt = np.linalg.svd(Xc, full_matrices=False)
-    components = Vt[:k]               # (k, p)
-    scores     = U[:, :k] * S[:k]     # (n, k)
-    explained  = (S**2) / (X.shape[0] - 1)
-    ratio      = explained[:k] / explained.sum()
-    return scores, components, ratio
-```
-
-### Randomized PCA (large p)
-```python
-from sklearn.decomposition import PCA
-pca = PCA(n_components=50, svd_solver="randomized", random_state=0).fit(X)
-# 매 O(n p k) cost — 매 huge p 의 effective.
-```
-
-### Incremental PCA (out-of-core)
-```python
-from sklearn.decomposition import IncrementalPCA
-ipca = IncrementalPCA(n_components=20, batch_size=2048)
-for chunk in batches(X, 2048):
-    ipca.partial_fit(chunk)
-Z = ipca.transform(X)
-```
-
-### Reconstruction & error
-```python
-X_hat = pca.inverse_transform(pca.transform(X))
-recon_err = np.linalg.norm(X - X_hat) / np.linalg.norm(X)
-```
-
-### Scree / elbow plot
-```python
-import matplotlib.pyplot as plt
-ev = pca.explained_variance_ratio_
-plt.plot(np.arange(1, len(ev)+1), ev.cumsum(), marker="o")
-plt.axhline(0.95, ls="--"); plt.xlabel("k"); plt.ylabel("cum. variance")
-```
-
-### Whitening for downstream classifier
-```python
-PCA(n_components=64, whiten=True).fit_transform(X)
-# 매 unit-variance, 매 decorrelated → 매 SVM/logistic baseline 향상.
-```
-
-## 매 결정 기준
-| 상황 | Approach |
-|---|---|
-| 매 small n, p | Full SVD PCA |
-| 매 large p, moderate k | Randomized SVD |
-| 매 streaming / OOC data | Incremental PCA |
-| 매 nonlinear manifold | Kernel PCA, UMAP, t-SNE 의 대신 |
-| 매 sparse / count data | TruncatedSVD (no centering) |
-| 매 outlier-heavy | Robust PCA (RPCA), or median-centering |
-
-**기본값**: 매 StandardScaler → PCA(n_components=0.95, svd_solver="auto").
+> **이 문서는 [[Principal Component Analysis]] 의 중복본입니다.** Canonical 문서로 redirect.

 ## 🔗 Graph
- 부모: [[Linear-Algebra-Foundations]] · [[Singular-Value-Decomposition]] · [[Eigenvalues-and-Eigenvectors]]
- 변형: [[PCA-and-Dimension-Reduction]] · [[Kernel PCA]] · [[Sparse PCA]]
- 응용: [[Multivariate-Analysis]] · [[Signal-Processing-Foundations]] · [[Genomics PCA]]
- Adjacent: [[t-SNE]] · [[UMAP]] · [[Autoencoders]]
+- 부모: [[Principal Component Analysis]] (canonical)

-## 🤖 LLM 활용
-**언제**: 매 dense numeric features 의 linear-correlated 의 visualize / denoise / compress.
-**언제 X**: 매 nonlinear manifold (rolled / curved) — 매 UMAP / t-SNE / autoencoder 의 사용. 매 categorical / sparse count — 매 MCA / TruncatedSVD.
-
-## ❌ 안티패턴
- **No mean-centering**: 매 first PC 의 just mean 의 direction 의 됨.
- **Scaling 무시**: 매 unit-mismatched features (mm vs kg) 의 dominate.
- **Top-k 의 magic number**: 매 scree / cum-variance 의 검토 없이 k 의 hardcode.
- **Test set leakage**: 매 fit on full data 후 split — fit 의 train 만.
- **Interpreting PCs as "factors"**: 매 PCA ≠ Factor Analysis (FA).
-
-## 🧪 검증 / 중복
- Verified (Hastie *ESL* 2e §14.5; Bishop *PRML* §12.1; scikit-learn docs 1.5).
- 매 SVD path 의 numerically stable; 매 covariance-eigendecomp 의 ill-conditioned cases 에 worse.
- 신뢰도 A.
-
-## 🕓 Changelog
+## 🕓 변경 이력
 | 날짜 | 변경 |
 |---|---|
-| 2026-05-08 | Phase 1 |
-| 2026-05-10 | Manual cleanup — SVD/randomized/incremental PCA full spec |
+| 2026-05-20 | 중복 병합 — canonical 문서로 redirect |