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TF-IDF gives a word more weight when it appears often in one document but occurs in relatively few documents across the collection. You can calculate it by multiplying a term’s frequency in a document by an inverse document frequency (IDF) weight computed across the corpus. This guide works through the calculation and a small Python implementation, then explains why its numbers may differ from scikit-learn’s.
What TF-IDF measures
TF-IDF stands for term frequency–inverse document frequency. It is a weighting scheme that combines two signals:
- Term frequency (TF): how often a term appears in a particular document.
- Inverse document frequency (IDF): how informative the term is across the corpus.
A frequent term in one document can be useful for describing that document. But if the term appears in almost every document, it does little to distinguish one document from another. IDF reduces the influence of such corpus-wide terms. A term that appears in fewer documents receives a larger IDF weight.
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Calculate TF-IDF by hand
Consider three documents after consistent lowercasing and tokenization:
- Document 1:
red cat cat - Document 2:
red dog - Document 3:
blue dog
Use raw term counts for TF and the unsmoothed formula IDF(t) = ln(n / df(t)), where n is the number of documents. This is one common teaching convention, not a universal definition.
1. Count terms in each document
The vocabulary is blue, cat, dog, and red. The term counts are:
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| Document | blue | cat | dog | red |
|---|---|---|---|---|
| 1 | 0 | 2 | 0 | 1 |
| 2 | 0 | 0 | 1 | 1 |
| 3 | 1 | 0 | 1 | 0 |
2. Count document frequency and compute IDF
There are three documents. blue and cat each appear in one document; dog and red each appear in two. With the chosen formula, their weights are:
| Term | Document frequency | IDF calculation | IDF |
|---|---|---|---|
| blue | 1 | ln(3 / 1) |
1.099 |
| cat | 1 | ln(3 / 1) |
1.099 |
| dog | 2 | ln(3 / 2) |
0.405 |
| red | 2 | ln(3 / 2) |
0.405 |
The logarithm values are rounded to three decimal places. The less widely shared words, blue and cat, receive higher weights.
3. Multiply TF by IDF
Document 1 has a raw count of two for cat and one for red. Its weighted values are therefore 2 × 1.099 = 2.198 for cat and 1 × 0.405 = 0.405 for red; its other terms have zero counts. The resulting vector in vocabulary order is [0, 2.198, 0, 0.405]. The same corpus-wide IDF values are applied to the counts in Documents 2 and 3.
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Implement a transparent version in Python
This example uses only Python’s standard library. It lowercases text and splits on whitespace, uses raw counts, computes unsmoothed natural-log IDF, and leaves vectors unnormalized. Those choices keep each stage visible; they are not meant to reproduce every library’s defaults.
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def tokenize(text):
return text.lower().split()
def fit_tfidf(documents):
tokenized = [tokenize(doc) for doc in documents]
vocabulary = sorted({term for doc in tokenized for term in doc})
document_frequency = Counter()
for doc in tokenized:
document_frequency.update(set(doc)) # once per term per document
n_documents = len(tokenized)
idf = {
term: math.log(n_documents / document_frequency[term])
for term in vocabulary
}
vectors = []
for doc in tokenized:
counts = Counter(doc)
vectors.append({
term: counts[term] * idf[term]
for term in vocabulary
})
return vocabulary, idf, vectorsAdd import math at the top of the snippet so math.log is available. For the three-document example, the vocabulary order is alphabetical, and the first result vector is {'blue': 0.0, 'cat': 2.197..., 'dog': 0.0, 'red': 0.405...}.
Transform later documents with the fitted model
For consistent features, retain the vocabulary and IDF learned from the fitting corpus. Do not recalculate them for each new document or batch: doing so changes the feature weights and can change the meaning of vector positions. Terms not present in the fitted vocabulary are ignored in this compact example.
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def transform_tfidf(documents, vocabulary, idf):
vectors = []
for text in documents:
counts = Counter(tokenize(text))
vectors.append({
term: counts[term] * idf[term]
for term in vocabulary
})
return vectorsTo use both snippets together, include import math and from collections import Counter once at the top. This simple tokenizer does not strip punctuation, handle multiword features, or apply stop-word filtering. Real applications should choose preprocessing deliberately and apply the same rules during fitting and transformation.
Why this differs from scikit-learn
scikit-learn’s TfidfVectorizer combines count vectorization and TF-IDF transformation. Its documented defaults use raw term counts, smoothed IDF, an additive offset, and L2 normalization. The default smoothed IDF is log((1 + n) / (1 + df(t))) + 1. As the scikit-learn feature extraction documentation explains, smoothing adds one to the numerator and denominator as if an extra document containing every term once had been seen; this prevents zero divisions.
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| Choice | Teaching implementation above | scikit-learn documented defaults |
|---|---|---|
| Term frequency | Raw counts | Raw counts; sublinear_tf=True changes this to 1 + log(tf) |
| IDF formula | ln(n / df(t)), no smoothing or offset |
log((1 + n) / (1 + df(t))) + 1 |
| Vector normalization | None | L2 |
| Preprocessing and vocabulary | Lowercase, whitespace split, vocabulary from fitting corpus | Configurable preprocessing, tokenization, stop words, and n-gram range |
| Feature space for later inputs | Reuse fitted vocabulary and IDF | Fit once, then transform later inputs with the fitted vectorizer |
When matching library output, align preprocessing and vocabulary as well as the formula. Differences in token boundaries, punctuation handling, stop words, n-grams, term-frequency scaling, smoothing, offset, and normalization can all change values or feature positions. See the TfidfVectorizer API reference for the documented parameters and fit/transform behavior.
When normalization matters
Without normalization, documents with more terms or repeated terms can have larger vector magnitudes. L2 normalization divides each nonzero vector by its Euclidean length. The normalized vector has unit length, and its dot product with another normalized vector equals cosine similarity. This is useful when comparing documents by direction (relative term weights) rather than by overall length.
Further reading
For a deeper treatment of term weighting and information retrieval, Stanford’s Introduction to Information Retrieval is an optional textbook; it is not required to implement the example here.
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