# Q2b · Lexical similarity and cosine

Subject: Natural Language Processing

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/nlp/#tee/papers/legacy-f24/q2b

Canonical: https://deep-learning-study-room.vercel.app/read/nlp/tee/papers/legacy-f24--q2b/

Previous examination · complete worked answers

**Question. Explain the need for lexical similarity and illustrate cosine similarity.** [4 marks]

### Answer

Similarity supports retrieval, clustering, duplicate detection and semantic matching. Choose a representation first: character overlap measures spelling; context embeddings approximate semantic relatedness. An illustrative cosine computation follows; these vectors are chosen to explain the method, not given exam data.

### Given

u=[1, 1, 0]; v=[1, 0, 1]

### To find

Cosine similarity in the given coordinate order.

### Formula: which one and why



$$
\cos(u,v)=\frac{u\cdot v}{\|u\|\|v\|}
$$



### Step 1. Multiply matching coordinates

1×1 + 1×0 + 0×1 = 1

### Step 2. Calculate both squared lengths

u: 1² + 1² + 0² = 2; v: 1² + 0² + 1² = 2

### Step 3. Take square roots and divide

1 / (√2 × √2) = 0.500000000

### Final answer

**Cosine=0.500000000.** This measures direction, not a probability.