TF-IDF TF-IDF 詞頻分析
Released已發布Implement TF-IDF scoring to measure term importance relative to a document corpus. Use this skill when the user needs to rank documents by keyword relevance, extract important terms from text, or build a basic search relevance engine — even if they say 'find relevant documents', 'keyword extraction', or 'term importance'.
演算法技能：TF-IDF 分析與應用。
Overview概述
TF-IDF (Term Frequency–Inverse Document Frequency) scores term importance as TF(t,d) × IDF(t). High scores mean a term is frequent in a document but rare across the corpus. Computes in O(N × V) where N is documents and V is vocabulary size.
When to Use使用時機
Trigger conditions:
- Ranking documents by keyword relevance
- Extracting distinguishing terms from documents
- Building lightweight search without ML models
When NOT to use:
- When semantic similarity matters (use embeddings instead)
- When you need ranking with link authority (combine with PageRank)
Algorithm 演算法
IRON LAW: TF-IDF Measures RELATIVE Importance
- A term with high TF but low IDF is common, NOT important
- TF-IDF = TF(t,d) × log(N / DF(t))
- A term appearing in ALL documents has IDF = 0 → score = 0
Phase 1: Input Validation
Tokenize documents, apply lowercasing, remove stop words. Build vocabulary. Gate: All documents tokenized, vocabulary size reasonable.
Phase 2: Core Algorithm
- Compute TF(t,d) for each term in each document (raw count, log-normalized, or boolean)
- Compute IDF(t) = log(N / DF(t)) where DF(t) = number of documents containing term t
- Compute TF-IDF(t,d) = TF(t,d) × IDF(t)
- Optionally L2-normalize document vectors for cosine similarity
Phase 3: Verification
Check: terms appearing in all documents have IDF ≈ 0. Rare terms have high IDF. Gate: Score distribution is reasonable; common words score low.
Phase 4: Output
Return scored terms per document or ranked documents per query.
Output Format輸出格式
{
"query_results": [{"document": "doc_id", "score": 0.73, "matching_terms": ["term1", "term2"]}],
"metadata": {"corpus_size": 1000, "vocabulary_size": 5000, "tf_variant": "log_normalized"}
}
Examples範例
Sample I/O
Input: Corpus: ["the cat sat", "the dog sat", "the cat played"], Query: "cat" Expected: TF("cat", doc1)=1/3, DF("cat")=2, IDF=log(3/2)=0.405. TF-IDF(doc1)=0.135, TF-IDF(doc3)=0.135, TF-IDF(doc2)=0
Edge Cases
| Input | Expected | Why |
|---|---|---|
| Term in all docs | Score = 0 | IDF = log(N/N) = 0 |
| Term in one doc | Highest IDF | log(N/1) = log(N) |
| Empty document | All scores = 0 | No terms to score |
Gotchas注意事項
- Stop words matter: Without stop word removal, "the", "is", "a" dominate TF but have zero IDF. Preprocess properly.
- TF variant choice: Raw count, log(1+count), or boolean TF produce very different rankings. Log normalization prevents long documents from dominating.
- IDF smoothing: Add 1 to denominator to avoid division by zero for unknown query terms: IDF = log(N / (DF+1)) + 1.
- Not semantic: "car" and "automobile" are treated as completely different terms. TF-IDF has no concept of synonymy.
- Corpus dependency: IDF values change when the corpus changes. Adding documents alters all scores.
References參考資料
- For BM25 (improved TF-IDF), see
references/bm25-comparison.md - For efficient inverted index implementation, see
references/inverted-index.md