Minkowski distance measures separation between numeric records by aggregating powered coordinate differences. Its power parameter selects related metrics: power 1 gives Manhattan distance, power 2 gives Euclidean distance, and larger powers emphasize the largest feature differences. section 9.7.1
Changing the power changes how coordinate differences influence the result:
- Manhattan distance sums absolute coordinate differences, treating each feature difference directly. section 9.7.1
- Euclidean distance squares differences before aggregation, so unusually large differences receive more influence. section 9.7.1
- Higher powers increase that emphasis; the limiting infinity-power case is Chebyshev distance, determined by the maximum difference. section 9.7.1
Two three-feature records
For [0.1, 0.6, 0.2] and [0.5, 0.4, 0.7], the coordinate differences are 0.4, 0.2, and 0.5. Manhattan distance is 1.1; Euclidean distance applies squared differences and a square root, while other powers provide alternative emphasis. section 9.7.1
