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Geometric median — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Geometric_median
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T16:43:21.715Z
SHA-256 of the archived text: 3bf4c9c8785d9512cffcc6c563c5bd5baf06de27ed84908f90ec1ae065183562
Stable URL of this page: https://metraipolis.com/documento/dc_cb57dbfc278d

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Geometric median — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Geometric_median (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_cb57dbfc278d (Metraipolis archive dc_cb57dbfc278d, sha256 3bf4c9c8785d9512cffcc6c563c5bd5baf06de27ed84908f90ec1ae065183562)

BibTeX

@misc{dccb57dbfc278d,
  title = {Geometric median — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Geometric_median},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_cb57dbfc278d; sha256 3bf4c9c8785d9512cffcc6c563c5bd5baf06de27ed84908f90ec1ae065183562},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Geometric_median. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances or absolute differences for one-dimensional data. It is also known as the spatial median, Euclidean minisum point, Torricelli point, or 1-median. It provides a measure of central tendency in higher dimensions and it is a standard problem in facility location, i.e., locating a facility to minimize the cost of transportation. The geometric median is an important estimator of location in statistics, because it minimizes the sum of the L2 distances of the samples. It is to be compared to the mean, which minimizes the sum of the squared L2 distances; and to the coordinate-wise median which minimizes the sum of the L1 distances. The more general k-median problem asks for the location of k cluster centers minimizing the sum of L2 distances from each sample point to its nearest center. The special case of the problem for three points in the plane (that is, m = 3 and n = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli. Its solution is now known as the Fermat point of the triangle formed by the three sample points. The geometric median may in turn be generalized to the problem of minimizing the sum of weighted distances, known as the Weber problem after Alfred Weber's discussion of the problem in his 1909 book on facility location. Some sources instead call Weber's problem the Fermat–Weber problem, but others use this name for the unweighted geometric median problem. Wesolowsky (1993) provides a survey of the geometric median problem. See Fekete, Mitchell & Beurer (2005) for generalizations of the problem to non-discrete point sets.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Geometric median» — https://en.wikipedia.org/wiki/Geometric_median
Wikidata Q5535496 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5535496
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Geometric_median?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1362724658, consultata il 2026-10-06T15:18:45.046Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 8476f88e9ed349ab3cdd272470a49828c6bf51b1e26964d382fc76e9c4ae35f6