Natural Language Processing · TEE · papers
Q7b · Distributional hypothesis and cosine
2022-11-22 · final · recovered AI paper
Previous examination · complete worked answers
Question. Justify “You shall know a word by the company it keeps.” Calculate cosine similarity of w₁=[0.2,0.1,0.3,0.4] and w₂=[0.3,0,0.2,0.5]. [10 marks]
Answer
Words occurring in similar contexts often have related meanings; vectors encode their context distributions. This is a statistical tendency, not proof that every similar-context pair is synonymous—antonyms can share contexts too.
Given
u=[0.2, 0.1, 0.3, 0.4]; v=[0.3, 0, 0.2, 0.5]
To find
Cosine similarity in the given coordinate order.
Formula: which one and why
LaTeX: \cos(u,v)=\frac{u\cdot v}{\|u\|\|v\|}Step 1. Multiply matching coordinates
0.2×0.3 + 0.1×0 + 0.3×0.2 + 0.4×0.5 = 0.32
Step 2. Calculate both squared lengths
u: 0.2² + 0.1² + 0.3² + 0.4² = 0.30000000000000004; v: 0.3² + 0² + 0.2² + 0.5² = 0.38
Step 3. Take square roots and divide
0.32 / (√0.30000000000000004 × √0.38) = 0.947758204
Final answer
Cosine=0.947758204. This measures direction, not a probability.