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

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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)

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)

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)

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)

# 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)

# 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)

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 · 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