docs(10_Wiki): Topic_Business/General/Graphic/Programming을 Topics/ 하위로 이동
최상위 10_Wiki/Topic_*였던 4개 카테고리 폴더를 10_Wiki/Topics/Topic_* 로 재배치. 콘텐츠 변경 없음(순수 폴더 이동) — Topics/ 하위 나머지 폴더는 이미 지난 커밋에서 전부 정리된 상태(잔존 항목은 에이전트 운영 상태 및 사용자가 보존을 요청한 업데이트0615/무제 3.canvas 뿐).
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Antigravity Agent
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---
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id: wiki-2026-0508-dimensionality-reduction
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title: Dimensionality Reduction
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [PCA, t-SNE, UMAP, autoencoder, curse of dimensionality, feature extraction]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.93
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verification_status: applied
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tags: [dimensionality-reduction, pca, tsne, umap, autoencoder, visualization, manifold-learning]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: scikit-learn / umap-learn / PyTorch
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---
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# Dimensionality Reduction
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## 매 한 줄
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> **"매 high-dim 의 essence 의 low-dim"**. 매 PCA (linear) → 매 t-SNE / UMAP (nonlinear, 시각화) → 매 Autoencoder / VAE (deep). 매 modern: 매 embedding (CLIP, sentence-transformers) 의 implicit dim reduction.
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## 매 핵심 method
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### Linear
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#### PCA (Principal Component Analysis)
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- 매 variance 의 maximum direction.
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- 매 orthogonal axis.
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- 매 SVD.
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- 매 fast + interpretable.
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#### LDA (Linear Discriminant Analysis)
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- 매 class separation 의 maximize.
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- 매 supervised.
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#### Factor Analysis
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- 매 latent factor 의 explain variance.
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### Nonlinear (manifold)
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#### t-SNE (Maaten 2008)
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- 매 local neighborhood 의 preserve.
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- 매 visualization 강.
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- 매 global structure 의 weak.
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- 매 stochastic.
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#### UMAP (McInnes 2018)
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- 매 t-SNE 의 successor.
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- 매 faster + 매 global structure 도 better.
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- 매 default for high-dim viz.
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#### Isomap
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- 매 geodesic distance 의 preserve.
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#### LLE (Locally Linear Embedding).
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### Neural
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#### Autoencoder
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- 매 bottleneck 의 dim reduce.
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#### VAE (Variational AE)
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- 매 probabilistic.
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#### Self-Supervised Embedding
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- 매 CLIP, BERT, sentence-transformers.
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- 매 implicit dim reduction.
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### 매 PaCMAP / TriMap (recent)
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- 매 UMAP 의 variant.
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- 매 better global structure.
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### 매 응용
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1. **Visualization** (2D / 3D): 매 t-SNE, UMAP.
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2. **Speed** (preprocess): 매 PCA.
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3. **Anomaly detection**: 매 autoencoder.
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4. **Feature extraction**: 매 embedding.
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5. **Compression**: 매 quantization + 매 embed.
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6. **Clustering preprocessing**.
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7. **RAG** (vector DB): 매 PCA / quantization.
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### 매 curse of dimensionality
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- 매 distance 의 meaningless.
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- 매 sparsity in 매 high-dim.
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- 매 sample requirement 의 exponential.
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## 💻 패턴
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### PCA (sklearn)
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```python
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from sklearn.decomposition import PCA
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from sklearn.preprocessing import StandardScaler
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X_scaled = StandardScaler().fit_transform(X)
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pca = PCA(n_components=0.95) # 매 95% variance 의 keep
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X_reduced = pca.fit_transform(X_scaled)
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print(f'Original: {X.shape[1]}, reduced: {pca.n_components_}')
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print(f'Explained variance: {pca.explained_variance_ratio_.cumsum()}')
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```
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### t-SNE
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```python
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from sklearn.manifold import TSNE
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tsne = TSNE(
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n_components=2,
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perplexity=30,
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n_iter=1000,
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random_state=42,
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)
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X_2d = tsne.fit_transform(X[:5000]) # 매 t-SNE 의 slow → 매 sample
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```
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### UMAP (modern)
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```python
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import umap
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reducer = umap.UMAP(
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n_components=2,
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n_neighbors=15,
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min_dist=0.1,
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metric='cosine', # 매 embedding 에 좋음
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random_state=42,
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)
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X_2d = reducer.fit_transform(X)
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```
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### Autoencoder (PyTorch)
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```python
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import torch.nn as nn
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class AE(nn.Module):
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def __init__(self, input_dim, latent_dim=32):
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super().__init__()
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self.encoder = nn.Sequential(
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nn.Linear(input_dim, 128), nn.ReLU(),
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nn.Linear(128, 64), nn.ReLU(),
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nn.Linear(64, latent_dim),
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)
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self.decoder = nn.Sequential(
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nn.Linear(latent_dim, 64), nn.ReLU(),
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nn.Linear(64, 128), nn.ReLU(),
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nn.Linear(128, input_dim),
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)
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def forward(self, x):
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z = self.encoder(x)
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return self.decoder(z), z
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# 매 latent 의 use
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model = AE(input_dim=784)
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# ... train ...
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_, latent = model(X_test)
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```
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### Visualization combo (UMAP + scatter)
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```python
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import matplotlib.pyplot as plt
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X_2d = umap.UMAP().fit_transform(X)
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plt.figure(figsize=(10, 8))
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plt.scatter(X_2d[:, 0], X_2d[:, 1], c=labels, cmap='tab10', alpha=0.5, s=10)
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plt.colorbar()
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plt.title('UMAP projection')
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plt.show()
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```
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### PCA for speed (vector DB preprocessing)
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```python
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from sklearn.decomposition import PCA
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import faiss
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# 매 매 768 의 OpenAI embedding → 매 256
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embeddings = get_embeddings(documents)
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pca = PCA(n_components=256)
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reduced = pca.fit_transform(embeddings).astype('float32')
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# 매 Faiss
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index = faiss.IndexFlatIP(256)
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index.add(reduced)
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```
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### Quantization (vector DB modern)
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```python
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import faiss
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dim = 768
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quantizer = faiss.IndexFlatIP(dim)
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index = faiss.IndexIVFPQ(quantizer, dim, nlist=100, m=8, nbits=8)
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# 매 8 byte 의 768-dim 의 represent — 매 매 100× compression.
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index.train(embeddings_np)
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index.add(embeddings_np)
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```
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### Word2Vec / CLIP-style (implicit reduction)
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```python
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from sentence_transformers import SentenceTransformer
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model = SentenceTransformer('all-MiniLM-L6-v2') # 매 384-dim
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embeddings = model.encode(sentences)
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# 매 매 sentence (potentially infinite words) → 매 384-dim.
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```
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### Reconstruction error (anomaly)
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```python
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def detect_anomaly(model, X, threshold):
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X_recon, _ = model(X)
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error = ((X_recon - X) ** 2).mean(dim=1)
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return error > threshold
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```
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### Choose dimension (elbow / cumvar)
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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pca = PCA().fit(X_scaled)
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cumvar = np.cumsum(pca.explained_variance_ratio_)
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plt.plot(cumvar)
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plt.xlabel('Component')
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plt.ylabel('Cumulative variance')
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plt.axhline(0.95, color='r', linestyle='--')
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plt.show()
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n_components = np.argmax(cumvar >= 0.95) + 1
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```
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### Manifold visualization comparison
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```python
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def viz_compare(X, labels):
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fig, axes = plt.subplots(1, 3, figsize=(20, 6))
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for ax, (name, reducer) in zip(axes, [
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('PCA', PCA(n_components=2)),
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('t-SNE', TSNE(n_components=2, random_state=42)),
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('UMAP', umap.UMAP(n_components=2, random_state=42)),
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]):
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proj = reducer.fit_transform(X)
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ax.scatter(proj[:, 0], proj[:, 1], c=labels, cmap='tab10', s=5)
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ax.set_title(name)
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```
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## 매 결정 기준
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| 상황 | Method |
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|---|---|
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| Speed (preprocess) | PCA |
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| Visualization | UMAP |
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| Cluster preserve | UMAP |
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| Variance interpret | PCA |
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| Class-aware | LDA |
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| Text → embedding | Sentence-transformer |
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| Image → embedding | CLIP |
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| Vector DB compress | PCA / PQ quantization |
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| Anomaly | Autoencoder |
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| Generative | VAE |
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**기본값**: PCA (preprocess) + UMAP (viz) + embedding (semantic).
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## 🔗 Graph
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- 부모: [[Feature Engineering|Feature-Engineering]]
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- 변형: [[PCA]] · [[t-SNE]] · [[UMAP]] · [[Autoencoder]] · [[VAE]]
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- 응용: [[CLIP]] · [[Sentence-Transformers]] · [[Faiss]] · [[Anomaly-Detection]]
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- Adjacent: [[Auto-Encoding]] · [[Bag of Words (BoW)]] · [[Bias vs Variance Trade-off]]
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## 🤖 LLM 활용
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**언제**: 매 visualization. 매 vector DB. 매 cluster preprocessing. 매 anomaly detection.
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**언제 X**: 매 already low-dim. 매 lossless 필수.
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## ❌ 안티패턴
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- **PCA without standardize**: 매 wrong principal component.
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- **t-SNE 의 cluster size 의 interpret**: 매 not preserved.
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- **UMAP 의 distance 의 absolute interpret**: 매 local 만.
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- **Too aggressive reduction**: 매 information loss.
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- **Forget train-test split**: 매 leakage in PCA.
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## 🧪 검증 / 중복
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- Verified (Jolliffe PCA, van der Maaten t-SNE, McInnes UMAP).
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- 신뢰도 A.
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- Related: [[Auto-Encoding]] · [[Bag of Words (BoW)]] · [[CLIP]] · [[Sentence-Transformers]] · [[Bias vs Variance Trade-off]].
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — methods + 매 PCA / t-SNE / UMAP / AE / Faiss / quantization code |
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