# Q4b · Three-document TF–IDF

Subject: Natural Language Processing

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/nlp/#tee/papers/legacy-f23/q4b

Canonical: https://deep-learning-study-room.vercel.app/read/nlp/tee/papers/legacy-f23--q4b/

Previous examination · complete worked answers

**Question. Calculate TF–IDF for: (1) Inflation increased unemployment (2) Company increased sales (3) Fear increased pulse.** [10 marks]

### Answer

### Given

| Document | Original text |
| --- | --- |
| 1 | Inflation increased unemployment |
| 2 | Company increased sales |
| 3 | Fear increased pulse |

Stopwords: none supplied

### To find

BoW, IDF and TF–IDF

### Formula: which one and why

Use lowercase alphabetic tokens and exactly the stated stoplist. If no stoplist is supplied, retain function words. Adopt raw-count TF and natural-log IDF; the paper does not prescribe another TF/log convention.



$$
\mathrm{TFIDF}(w,d)=c(w,d)\ln\frac{N}{\mathrm{df}(w)}
$$



A term shared by all N documents has IDF ln(1)=0. Counts and TF–IDF weights are different representations.

### Step 1. Tokenize each document

| Document | Tokens |
| --- | --- |
| 1 | inflation, increased, unemployment |
| 2 | company, increased, sales |
| 3 | fear, increased, pulse |

### Step 2. Fix the vocabulary order

company, fear, increased, inflation, pulse, sales, unemployment

### Step 3. Count occurrences (Bag of Words)

| Document | company | fear | increased | inflation | pulse | sales | unemployment |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
| 2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 3 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |

### Step 4. Calculate document frequency and IDF

| Term | df | N / df | ln(N/df) |
| --- | --- | --- | --- |
| company | 1 | 3 | 1.098612289 |
| fear | 1 | 3 | 1.098612289 |
| increased | 3 | 1 | 0.000000000 |
| inflation | 1 | 3 | 1.098612289 |
| pulse | 1 | 3 | 1.098612289 |
| sales | 1 | 3 | 1.098612289 |
| unemployment | 1 | 3 | 1.098612289 |

### Step 5. Multiply each TF by its IDF

| Document | company | fear | increased | inflation | pulse | sales | unemployment |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | 0.000000 | 0.000000 | 0.000000 | 1.098612 | 0.000000 | 0.000000 | 1.098612 |
| 2 | 1.098612 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.098612 | 0.000000 |
| 3 | 0.000000 | 1.098612 | 0.000000 | 0.000000 | 1.098612 | 0.000000 | 0.000000 |

### Final answer

The final table is the TF–IDF matrix in the declared vocabulary order. A different explicitly stated log base rescales all IDFs; length-normalized TF changes each document scale.