TF-IDF

Overview

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

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

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

{
  "query_results": [{"document": "doc_id", "score": 0.73, "matching_terms": ["term1", "term2"]}],
  "metadata": {"corpus_size": 1000, "vocabulary_size": 5000, "tf_variant": "log_normalized"}
}

Examples

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

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.

Scripts

Script	Description	Usage
`scripts/tfidf.py`	Compute TF-IDF vectors, top terms per document, and query scoring	`python scripts/tfidf.py --help`

Run python scripts/tfidf.py --verify to execute built-in sanity tests.

References

For BM25 (improved TF-IDF), see references/bm25-comparison.md
For efficient inverted index implementation, see references/inverted-index.md

algo-seo-tfidf