Lesson 15 — Cosine similarity

Cosine similarity: same direction, not same size

Cosine similarity measures how much two vectors point the same way: 1 = same direction, 0 = unrelated, −1 = opposite. Formula: dot(a, b) / (norm(a) × norm(b)). Unlike distance, it ignores length — a short and a long text about the same topic still score high.

# [1, 1] and [2, 2] point the same way -> 1.0

Here each document is a word-count vector: how many times each word of a small vocabulary appears.

Why it matters: search engines, recommendation systems and AI "embeddings" all use cosine similarity to find related items.