# Q5A · Why TF–IDF is useful

Subject: Natural Language Processing

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/nlp/#tee/mocks/timed-reexam-2026/reexam-2026-q5a

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TEE · actual previous paper · 100 marks · 180 minutes

Question. Justify with an appropriate example the importance of TF-IDF technique in the document representation and information retrieval task. [10 marks]

### Answer

**TF–IDF** represents each document using weights that combine within-document term frequency with how unusual a term is across the collection. It supports information retrieval by giving larger weight to terms that are frequent in a document but not present in every document.

### Given

Use three short documents: D₁ = “solar energy solar”; D₂ = “wind energy”; D₃ = “energy policy”. Use raw-count TF and natural-log unsmoothed IDF. N = 3.

### To find

A TF–IDF representation illustrating why distinctive terms help retrieve relevant documents.

### Formula: which one and why



$$
\mathrm{TFIDF}(t,d)=C(t,d)\ln\frac{N}{\mathrm{df}(t)}
$$



C counts occurrences within a document; df counts documents containing the term. The logarithm reduces the scale of very large rarity ratios.

### Solution

### Step 1. Count term occurrences

| Term | D₁ | D₂ | D₃ | df |
| --- | --- | --- | --- | --- |
| solar | 2 | 0 | 0 | 1 |
| energy | 1 | 1 | 1 | 3 |
| wind | 0 | 1 | 0 | 1 |
| policy | 0 | 0 | 1 | 1 |

### Step 2. Calculate IDF



$$
\mathrm{IDF}(solar)=\mathrm{IDF}(wind)=\mathrm{IDF}(policy)=\ln3\approx1.098612
$$





$$
\mathrm{IDF}(energy)=\ln(3/3)=0
$$



### Step 3. Multiply each count by its IDF

| Term | D₁ weight | D₂ weight | D₃ weight |
| --- | --- | --- | --- |
| solar | 2 × 1.098612 = 2.197224 | 0 | 0 |
| energy | 0 | 0 | 0 |
| wind | 0 | 1.098612 | 0 |
| policy | 0 | 0 | 1.098612 |

### Step 4. Connect the representation to retrieval

A query containing “solar” matches D₁’s high solar coordinate. A query containing “wind” matches D₂. “energy” alone cannot distinguish these documents under this unsmoothed collection because it occurs in all three. A retrieval system can compare query and document vectors, commonly by cosine similarity.

### Final answer

TF–IDF preserves distinctive lexical evidence and reduces dominance by collection-wide frequent terms. D₁ is most relevant to a solar query under these features.

**Yaad rakho:** Document mein frequent + collection mein rare = high TF–IDF.

### Strengths and limits

The representation is sparse, interpretable and useful as a fast baseline. However, basic TF–IDF ignores word order and does not recognise synonyms or multiple word senses automatically. Its weights depend on the collection and on the chosen TF/IDF convention. Fit IDF on training or indexed documents, not on a hidden test set.