Mathematics for ML

Euclidean Distance, explained

Euclidean distance is the straight-line distance between two points in a vector space.
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Part of the Semantic Notion technical glossary.

Short Definition

Euclidean distance is the straight-line distance between two points in a vector space.

Intuition

It is the ordinary geometric distance you would measure with a ruler, generalized to many dimensions.

Technical Definition

Euclidean distance is the L2 norm of the difference between two vectors.

Example

Clustering algorithms may group points by Euclidean distance in feature space.

Common Misunderstandings

Euclidean distance can behave poorly in very high-dimensional spaces.
It is sensitive to feature scale.

Same Category

More from Mathematics for ML

Cosine SimilarityCosine similarity measures how similar two vectors are by comparing their direction rather than their magnitude.Cross-EntropyCross-entropy measures how well one probability distribution matches another, often a model prediction against a target label.Dot ProductThe dot product combines two vectors into a single number that reflects their alignment and magnitude.EigenvalueAn eigenvalue is the scaling factor applied to an eigenvector by a linear transformation.EigenvectorAn eigenvector is a nonzero vector whose direction stays the same under a linear transformation.EntropyEntropy measures uncertainty or information content in a probability distribution.

Related Reading

Essays that use this concept

Vector Search and RetrievalCosine Similarity vs Euclidean Distance vs Dot Product

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