Distance Metrics

Euclidean, Manhattan, and Cosine distance/similarity measures

Euclidean Distance

  • Straight-line distance between two points
  • $d(p,q) = \sqrt{\sum_{i=1}^{n}(p_i - q_i)^2}$

Manhattan Distance

  • Sum of absolute differences between coordinates
  • $d(p,q) = \sum_{i=1}^{n} p_i - q_i $

Cosine Similarity

  • Measures cosine of angle between two vectors
  • Range: [-1, 1] where 1 means identical
  • $\cos(\theta) = \frac{A \cdot B}{|A| \cdot |B|}$
  • Cosine distance: $d(p,q) = 1 - \cos(\theta)$