Cosine Similarity

Weight: 1.0

What It Does

Compares two code files by treating them as bags of tokens (words) and measuring the angle between their frequency vectors. Identical documents have cosine = 1; completely different documents have cosine = 0.

The Math

Given two documents represented as term-frequency vectors A and B:

similarity(A, B) = (A · B) / (‖A‖ × ‖B‖)

where:
  A · B    = Σ(aᵢ × bᵢ)       (dot product)
  ‖A‖     = √(Σ(aᵢ²))         (L2 norm)

Example

Given two code snippets:

File A: "int x = 5; int y = 10; return x + y;"
File B: "int a = 5; int b = 10; return a + b;"

After tokenization:

A: {int: 2, x: 2, 5: 1, y: 2, 10: 1, return: 1}
B: {int: 2, a: 2, 5: 1, b: 2, 10: 1, return: 1}

Shared tokens: int, 5, 10, return → significant overlap.

After identifier normalization (a preprocessing step), both become:

{int: 2, v0: 2, 5: 1, v1: 2, 10: 1, return: 1}

Now cosine similarity = 1.0 (identical).

Why It Works for Plagiarism Detection

Captures the overall “vocabulary” of a program
Insensitive to token ordering (reordering lines doesn’t help)
Combined with preprocessing (case fold, identifier normalize), it catches renamed-variable plagiarism

Limitations

Doesn’t capture structure — two programs with the same tokens in completely different order score identically
Short programs may score high by coincidence (few unique tokens)
That’s why Analogi uses multiple analyzers, not just cosine

Threshold

Only triggers when similarity > 0.6 (60%). Below this, most code is coincidentally similar due to language keywords.