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-similarity-metrics-in-ai
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title: Similarity Metrics in AI
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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: [Similarity Measures, Distance Metrics, Vector Similarity]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [similarity, embeddings, retrieval, vector-search]
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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: numpy/faiss/sentence-transformers
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---
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# Similarity Metrics in AI
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## 매 한 줄
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> **"매 similarity 의 metric choice 는 매 retrieval / clustering / matching quality 의 결정"**. 매 cosine 의 dominant 의 dense embedding semantic search, 매 Jaccard 의 set overlap, 매 edit distance 의 string fuzzy matching. 매 2026 의 modern stack 의 normalized cosine + ANN (HNSW/IVF-PQ) 의 standard.
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## 매 핵심
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### 매 Vector metrics
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- **Cosine similarity**: `dot(a,b) / (||a|| * ||b||)` — 매 magnitude-invariant. 매 embedding 의 default.
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- **Dot product**: 매 normalized embedding 의 cosine 과 equivalent. 매 faster (no division).
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- **Euclidean (L2)**: 매 raw distance. 매 cluster centroid / k-means 의 use.
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- **Manhattan (L1)**: 매 robust to outliers. 매 sparse feature 의 use.
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### 매 Set / String metrics
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- **Jaccard**: `|A ∩ B| / |A ∪ B|` — 매 set / token overlap.
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- **Levenshtein (edit distance)**: 매 character-level fuzzy match.
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- **Hamming**: 매 fixed-length binary / hash 의 distance.
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- **Tanimoto**: 매 chemistry / fingerprint similarity.
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### 매 응용
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1. **Semantic search** — sentence-transformer embedding + cosine + FAISS HNSW.
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2. **Deduplication** — MinHash + Jaccard 의 near-duplicate detection.
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3. **Recommendation** — user/item embedding cosine.
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4. **Fuzzy matching** — record linkage 의 Levenshtein / Jaro-Winkler.
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## 💻 패턴
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### Cosine similarity (numpy)
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```python
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import numpy as np
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def cosine_sim(a: np.ndarray, b: np.ndarray) -> float:
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return float(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b) + 1e-12))
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def cosine_matrix(A: np.ndarray, B: np.ndarray) -> np.ndarray:
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A_n = A / (np.linalg.norm(A, axis=1, keepdims=True) + 1e-12)
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B_n = B / (np.linalg.norm(B, axis=1, keepdims=True) + 1e-12)
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return A_n @ B_n.T
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```
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### Sentence embedding + FAISS (2026 stack)
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```python
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from sentence_transformers import SentenceTransformer
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import faiss
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import numpy as np
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model = SentenceTransformer("BAAI/bge-large-en-v1.5")
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docs = ["alpha doc", "beta doc", "gamma doc"]
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emb = model.encode(docs, normalize_embeddings=True).astype("float32")
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index = faiss.IndexHNSWFlat(emb.shape[1], 32)
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index.metric_type = faiss.METRIC_INNER_PRODUCT # cosine via normalized
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index.add(emb)
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q = model.encode(["alpha"], normalize_embeddings=True).astype("float32")
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D, I = index.search(q, k=3)
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```
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### Jaccard via MinHash (datasketch)
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```python
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from datasketch import MinHash, MinHashLSH
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def mh(tokens, num_perm=128):
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m = MinHash(num_perm=num_perm)
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for t in tokens:
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m.update(t.encode("utf-8"))
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return m
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lsh = MinHashLSH(threshold=0.7, num_perm=128)
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lsh.insert("doc1", mh("the quick brown fox".split()))
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lsh.insert("doc2", mh("the quick brown dog".split()))
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print(lsh.query(mh("the quick brown fox jumps".split())))
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```
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### Levenshtein (rapidfuzz)
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```python
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from rapidfuzz.distance import Levenshtein
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from rapidfuzz import fuzz, process
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print(Levenshtein.distance("kitten", "sitting")) # 3
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print(fuzz.ratio("apple inc.", "apple, inc")) # ~95
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choices = ["Acme Corp", "Apple Inc.", "Microsoft"]
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print(process.extractOne("aple", choices, scorer=fuzz.ratio))
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```
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### Euclidean vs cosine (when matters)
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```python
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# Cosine: angle only — magnitude ignored
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a = np.array([1.0, 0.0]); b = np.array([10.0, 0.0])
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# cosine(a,b) = 1.0 (identical direction)
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# euclidean(a,b) = 9.0 (very different magnitude)
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```
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### Hybrid retrieval (BM25 + dense)
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```python
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# 매 modern RAG 의 default — sparse + dense fusion
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from rank_bm25 import BM25Okapi
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import numpy as np
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tokenized = [d.split() for d in docs]
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bm25 = BM25Okapi(tokenized)
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sparse_scores = bm25.get_scores("alpha doc".split())
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dense_scores = (emb @ q.T).flatten()
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# Reciprocal Rank Fusion
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def rrf(rankings, k=60):
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scores = {}
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for ranking in rankings:
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for rank, doc_id in enumerate(ranking):
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scores[doc_id] = scores.get(doc_id, 0) + 1 / (k + rank)
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return sorted(scores.items(), key=lambda x: -x[1])
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```
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### Tanimoto (binary fingerprint)
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```python
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def tanimoto(a: np.ndarray, b: np.ndarray) -> float:
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inter = np.sum(a & b)
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union = np.sum(a | b)
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return inter / union if union else 0.0
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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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| Dense embedding | Cosine (or normalized dot) |
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| K-means / GMM | Euclidean |
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| Token / set overlap | Jaccard |
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| String fuzzy match | Levenshtein / Jaro-Winkler |
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| Binary fingerprint | Hamming / Tanimoto |
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| Large-scale ANN | HNSW (cosine) or IVF-PQ |
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**기본값**: normalized embedding + cosine + HNSW.
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## 🔗 Graph
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- 부모: [[Embeddings]] · [[Vector-Search]]
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- 응용: [[Semantic Search|Semantic-Search]] · [[Deduplication]] · [[RAG]]
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- Adjacent: [[Sentence-Transformers]] · [[FAISS]]
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## 🤖 LLM 활용
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**언제**: semantic similarity, paraphrase detection, dedup of LLM outputs, eval (semantic equivalence).
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**언제 X**: exact match required, ordinal / numeric distance — use direct comparison.
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## ❌ 안티패턴
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- **Unnormalized cosine**: 매 forgetting normalization → magnitude bias.
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- **L2 on sparse high-D**: 매 curse of dimensionality — cosine more robust.
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- **Single metric**: 매 hybrid (sparse + dense) 의 better recall.
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- **Brute force at scale**: >1M vectors 의 ANN required.
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## 🧪 검증 / 중복
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- Verified (FAISS docs, sentence-transformers, rapidfuzz).
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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 — full content with metric patterns + hybrid retrieval |
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