2nd/10_Wiki/Topics/AI_and_ML/Similarity-Metrics-in-AI.md

---
id: wiki-2026-0508-similarity-metrics-in-ai
title: Similarity Metrics in AI
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Similarity Measures, Distance Metrics, Vector Similarity]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [similarity, embeddings, retrieval, vector-search]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: numpy/faiss/sentence-transformers
---

# Similarity Metrics in AI

## 매 한 줄
> **"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.

## 매 핵심

### 매 Vector metrics
- **Cosine similarity**: `dot(a,b) / (||a|| * ||b||)` — 매 magnitude-invariant. 매 embedding 의 default.
- **Dot product**: 매 normalized embedding 의 cosine 과 equivalent. 매 faster (no division).
- **Euclidean (L2)**: 매 raw distance. 매 cluster centroid / k-means 의 use.
- **Manhattan (L1)**: 매 robust to outliers. 매 sparse feature 의 use.

### 매 Set / String metrics
- **Jaccard**: `|A ∩ B| / |A ∪ B|` — 매 set / token overlap.
- **Levenshtein (edit distance)**: 매 character-level fuzzy match.
- **Hamming**: 매 fixed-length binary / hash 의 distance.
- **Tanimoto**: 매 chemistry / fingerprint similarity.

### 매 응용
1. **Semantic search** — sentence-transformer embedding + cosine + FAISS HNSW.
2. **Deduplication** — MinHash + Jaccard 의 near-duplicate detection.
3. **Recommendation** — user/item embedding cosine.
4. **Fuzzy matching** — record linkage 의 Levenshtein / Jaro-Winkler.

## 💻 패턴

### Cosine similarity (numpy)
```python
import numpy as np

def cosine_sim(a: np.ndarray, b: np.ndarray) -> float:
    return float(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b) + 1e-12))

def cosine_matrix(A: np.ndarray, B: np.ndarray) -> np.ndarray:
    A_n = A / (np.linalg.norm(A, axis=1, keepdims=True) + 1e-12)
    B_n = B / (np.linalg.norm(B, axis=1, keepdims=True) + 1e-12)
    return A_n @ B_n.T
```

### Sentence embedding + FAISS (2026 stack)
```python
from sentence_transformers import SentenceTransformer
import faiss
import numpy as np

model = SentenceTransformer("BAAI/bge-large-en-v1.5")
docs = ["alpha doc", "beta doc", "gamma doc"]
emb = model.encode(docs, normalize_embeddings=True).astype("float32")

index = faiss.IndexHNSWFlat(emb.shape[1], 32)
index.metric_type = faiss.METRIC_INNER_PRODUCT  # cosine via normalized
index.add(emb)

q = model.encode(["alpha"], normalize_embeddings=True).astype("float32")
D, I = index.search(q, k=3)
```

### Jaccard via MinHash (datasketch)
```python
from datasketch import MinHash, MinHashLSH

def mh(tokens, num_perm=128):
    m = MinHash(num_perm=num_perm)
    for t in tokens:
        m.update(t.encode("utf-8"))
    return m

lsh = MinHashLSH(threshold=0.7, num_perm=128)
lsh.insert("doc1", mh("the quick brown fox".split()))
lsh.insert("doc2", mh("the quick brown dog".split()))
print(lsh.query(mh("the quick brown fox jumps".split())))
```

### Levenshtein (rapidfuzz)
```python
from rapidfuzz.distance import Levenshtein
from rapidfuzz import fuzz, process

print(Levenshtein.distance("kitten", "sitting"))  # 3
print(fuzz.ratio("apple inc.", "apple, inc"))      # ~95

choices = ["Acme Corp", "Apple Inc.", "Microsoft"]
print(process.extractOne("aple", choices, scorer=fuzz.ratio))
```

### Euclidean vs cosine (when matters)
```python
# Cosine: angle only — magnitude ignored
a = np.array([1.0, 0.0]); b = np.array([10.0, 0.0])
# cosine(a,b) = 1.0 (identical direction)
# euclidean(a,b) = 9.0 (very different magnitude)
```

### Hybrid retrieval (BM25 + dense)
```python
# 매 modern RAG 의 default — sparse + dense fusion
from rank_bm25 import BM25Okapi
import numpy as np

tokenized = [d.split() for d in docs]
bm25 = BM25Okapi(tokenized)
sparse_scores = bm25.get_scores("alpha doc".split())
dense_scores = (emb @ q.T).flatten()

# Reciprocal Rank Fusion
def rrf(rankings, k=60):
    scores = {}
    for ranking in rankings:
        for rank, doc_id in enumerate(ranking):
            scores[doc_id] = scores.get(doc_id, 0) + 1 / (k + rank)
    return sorted(scores.items(), key=lambda x: -x[1])
```

### Tanimoto (binary fingerprint)
```python
def tanimoto(a: np.ndarray, b: np.ndarray) -> float:
    inter = np.sum(a & b)
    union = np.sum(a | b)
    return inter / union if union else 0.0
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Dense embedding | Cosine (or normalized dot) |
| K-means / GMM | Euclidean |
| Token / set overlap | Jaccard |
| String fuzzy match | Levenshtein / Jaro-Winkler |
| Binary fingerprint | Hamming / Tanimoto |
| Large-scale ANN | HNSW (cosine) or IVF-PQ |

**기본값**: normalized embedding + cosine + HNSW.

## 🔗 Graph
- 부모: [[Embeddings]] · [[Vector-Search]]
- 응용: [[Semantic Search|Semantic-Search]] · [[Deduplication]] · [[RAG]]
- Adjacent: [[Sentence-Transformers]] · [[FAISS]]

## 🤖 LLM 활용
**언제**: semantic similarity, paraphrase detection, dedup of LLM outputs, eval (semantic equivalence).
**언제 X**: exact match required, ordinal / numeric distance — use direct comparison.

## ❌ 안티패턴
- **Unnormalized cosine**: 매 forgetting normalization → magnitude bias.
- **L2 on sparse high-D**: 매 curse of dimensionality — cosine more robust.
- **Single metric**: 매 hybrid (sparse + dense) 의 better recall.
- **Brute force at scale**: >1M vectors 의 ANN required.

## 🧪 검증 / 중복
- Verified (FAISS docs, sentence-transformers, rapidfuzz).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — full content with metric patterns + hybrid retrieval |