Euclidean Distance
also: L2 distance
Straight-line distance between two points/vectors — the intuitive “ruler” metric, sensitive to magnitude.
Euclidean distance is the straight-line distance between two points, computed as the square root of the summed squared differences of their coordinates — the everyday “ruler” notion of distance, generalized to high-dimensional vectors. It is a common metric for clustering and nearest-neighbor search.
Worked example: k-means and k-NN typically use Euclidean distance to decide which points are “close”; two embeddings are near if the straight-line gap between them is small. Gotcha: Euclidean distance is sensitive to magnitude and feature scale — a feature with a large range dominates unless you normalize — and in very high dimensions distances concentrate (everything becomes nearly equidistant, the curse of dimensionality), which is why cosine similarity is often preferred for text embeddings where direction matters more than length.