refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-k-means-clustering-foundations
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title: K-Means Clustering
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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: [k-means, clustering, k-means++, mini-batch, elbow method, silhouette]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.97
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verification_status: applied
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tags: [machine-learning, clustering, k-means, unsupervised, lloyd]
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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 / FAISS
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---
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# K-Means Clustering
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## 매 한 줄
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> **"매 K centroid 의 의 의 minimize within-cluster variance"**. Lloyd 1957. 매 simple, fast, scalable. 매 limitations: 매 spherical assumption, K 의 specify, local optimum. 매 modern: 매 k-means++, mini-batch, FAISS-based for billion-scale.
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## 매 핵심
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### 매 algorithm (Lloyd)
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1. 매 K centroids 의 init.
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2. **Assign**: 매 매 point 의 closest centroid.
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3. **Update**: 매 centroid = mean.
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4. 매 1-2 의 converge 의 의 의 repeat.
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### 매 init
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- **Random**: 매 worst.
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- **k-means++** (Arthur 2007): 매 spread out.
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- **Forgy**: 매 random K points.
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### 매 K selection
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- **Elbow** method.
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- **Silhouette** score.
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- **Gap statistic**.
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- **BIC / AIC** (Gaussian Mixture).
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### 매 응용
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1. **Customer segmentation**.
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2. **Image quantization** (color palette).
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3. **Anomaly** (distance from centroid).
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4. **Document clustering**.
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5. **Vector index** (FAISS IVF).
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## 💻 패턴
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### sklearn k-means
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```python
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from sklearn.cluster import KMeans
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km = KMeans(n_clusters=5, init='k-means++', n_init=10, random_state=0).fit(X)
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labels = km.labels_
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centroids = km.cluster_centers_
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```
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### Mini-batch (faster)
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```python
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from sklearn.cluster import MiniBatchKMeans
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km = MiniBatchKMeans(n_clusters=100, batch_size=1024).fit(X)
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```
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### Elbow method
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```python
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import matplotlib.pyplot as plt
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inertias = []
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ks = range(1, 15)
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for k in ks:
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km = KMeans(n_clusters=k, n_init=10).fit(X)
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inertias.append(km.inertia_)
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plt.plot(ks, inertias, 'o-')
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plt.xlabel('K'); plt.ylabel('Inertia')
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# 매 elbow point = 매 best K
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```
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### Silhouette
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```python
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from sklearn.metrics import silhouette_score
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for k in [3, 4, 5, 6, 7]:
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labels = KMeans(n_clusters=k, n_init=10).fit_predict(X)
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print(k, silhouette_score(X, labels))
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# 매 closer to 1 = 매 better
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```
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### k-means++ init (manual)
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```python
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import numpy as np
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def kmeans_pp_init(X, k):
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centers = [X[np.random.randint(len(X))]]
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for _ in range(k - 1):
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d2 = np.array([min(np.linalg.norm(x - c) ** 2 for c in centers) for x in X])
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probs = d2 / d2.sum()
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cumprob = probs.cumsum()
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idx = np.searchsorted(cumprob, np.random.rand())
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centers.append(X[idx])
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return np.array(centers)
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```
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### Custom Lloyd (educational)
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```python
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def kmeans_lloyd(X, k, max_iter=100):
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centers = X[np.random.choice(len(X), k, replace=False)]
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for _ in range(max_iter):
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# 매 assign
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dists = np.linalg.norm(X[:, None] - centers, axis=2)
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labels = dists.argmin(axis=1)
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# 매 update
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new_centers = np.array([X[labels == i].mean(axis=0) for i in range(k)])
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if np.allclose(centers, new_centers): break
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centers = new_centers
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return labels, centers
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```
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### FAISS k-means (large-scale)
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```python
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import faiss
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d = X.shape[1]
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kmeans = faiss.Kmeans(d, k=100, niter=20, gpu=True)
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kmeans.train(X.astype('float32'))
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centroids = kmeans.centroids
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_, labels = kmeans.index.search(X.astype('float32'), 1)
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```
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### Image color quantization
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```python
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def quantize_image(img, k=8):
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pixels = img.reshape(-1, 3)
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km = KMeans(n_clusters=k, n_init=3).fit(pixels)
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quantized = km.cluster_centers_[km.labels_]
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return quantized.reshape(img.shape).astype('uint8')
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```
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### Anomaly via distance
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```python
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def detect_anomaly(X, km, threshold=None):
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dists = np.linalg.norm(X - km.cluster_centers_[km.predict(X)], axis=1)
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if threshold is None: threshold = np.percentile(dists, 99)
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return dists > threshold
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```
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### Spherical k-means (text, cosine)
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```python
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def spherical_kmeans(X, k, max_iter=100):
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"""매 normalize → k-means 의 cosine equivalent."""
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X_norm = X / np.linalg.norm(X, axis=1, keepdims=True)
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return KMeans(n_clusters=k).fit(X_norm)
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```
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### Gaussian Mixture (alternative)
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```python
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from sklearn.mixture import GaussianMixture
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gmm = GaussianMixture(n_components=5, covariance_type='full').fit(X)
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labels = gmm.predict(X)
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# 매 vs k-means: 매 ellipsoidal cluster + soft assignment
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```
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### Scaling (always)
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```python
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from sklearn.preprocessing import StandardScaler
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X_scaled = StandardScaler().fit_transform(X)
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km = KMeans(n_clusters=5).fit(X_scaled)
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```
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### Dimensionality reduction first (high-D)
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```python
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from sklearn.decomposition import PCA
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X_reduced = PCA(n_components=50).fit_transform(X)
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km = KMeans(n_clusters=5).fit(X_reduced)
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```
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### Initialize from labels (semi-supervised)
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```python
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init_centers = np.array([X[y == c].mean(axis=0) for c in np.unique(y)])
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km = KMeans(n_clusters=len(init_centers), init=init_centers, n_init=1).fit(X)
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Small N | sklearn |
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| Large N | MiniBatch |
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| Massive N | FAISS |
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| Image | Color quantize |
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| Text | Spherical (normalized) |
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| Non-spherical | GMM / DBSCAN |
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**기본값**: 매 scale + k-means++ + 매 multiple n_init + 매 elbow / silhouette for K. 매 large = MiniBatch / FAISS.
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## 🔗 Graph
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- 부모: [[Clustering]]
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- 변형: [[k-means++]]
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- Adjacent: [[K-Nearest-Neighbors-K-NN]]
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## 🤖 LLM 활용
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**언제**: 매 segmentation. 매 EDA. 매 vector index.
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**언제 X**: 매 non-spherical / density-varying (use DBSCAN).
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## ❌ 안티패턴
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- **No scaling**: 매 dominant feature.
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- **K=2 default**: 매 wrong.
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- **Random init**: 매 use k-means++.
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- **K-means on non-spherical**: 매 wrong.
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## 🧪 검증 / 중복
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- Verified (Lloyd 1957, Arthur k-means++ 2007, FAISS docs).
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- 신뢰도 A.
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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 — Lloyd / ++/MiniBatch + 매 elbow / silhouette / FAISS / quantize code |
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