Euclidean Distance (L2 Distance)

Fundamental similarity metric for vector search measuring the cosine of the angle between vectors. Range from -1 to 1, with 1 indicating identical direction regardless of magnitude.

Similarity metric computing sum of element-wise products between vectors. Efficient for normalized vectors, equivalent to cosine similarity when vectors are unit length.

Distance metric for binary vectors counting the number of positions at which corresponding bits differ, computed efficiently using XOR and popcount operations for ultra-fast similarity search.

Vector similarity metric measuring both directional similarity and magnitude of vectors. Used by many LLMs for training and equivalent to cosine similarity for normalized data. Reports both angle and magnitude information.

Vector distance metric calculating the sum of absolute differences between vector components. Measures grid-like distance and is robust to outliers, with faster calculation as data dimensionality increases.

Mathematical measures for comparing vector similarity including cosine similarity (directional), Euclidean distance (geometric), dot product (magnitude+direction), and Manhattan distance (grid-based) for AI and search applications.