ITPEC FE Subject B April 2024 Question 14

Computing cosine similarity between two vectors.

The function calcSim computes cosine similarity:

sxy ÷ √(sxx × syy)

where sxx = Σ(v1[i]²), syy = Σ(v2[i]²), sxy = Σ(v1[i] × v2[i]).

For v1 = {2, 2, 1, 0, 4} and v2 = {3, 1, 1, 1, 2}:

• •sxx = 4 + 4 + 1 + 0 + 16 = 25
• •syy = 9 + 1 + 1 + 1 + 4 = 16
• •sxy = 6 + 2 + 1 + 0 + 8 = 17

Result = 17 ÷ √(25 × 16) = 17 ÷ √400 = 17 ÷ 20 = 0.85 → rounded to first decimal place = 0.9

Why not others:
- (a)–(h) — do not match the computed value of 0.85, which rounds to 0.9
- (j) 1.0 — would mean identical direction vectors; these vectors differ

Key rule: Cosine similarity = Σ(x·y) ÷ √(Σx² · Σy²), ranges from 0 (orthogonal) to 1 (identical direction) for non-negative vectors.

AI-generated — may contain errors