Geometric median (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Geometric median" in English language version.

refsWebsite

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12doi.org

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5ams.org

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4books.google.com

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4nih.gov

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3jstor.org

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2web.archive.org

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2semanticscholar.org

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1dtic.mil

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1carleton.ca

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1harvard.edu

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1tudelft.nl

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1zbmath.org

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1vub.ac.be

low place

1purdue.edu

850^th place

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1jst.go.jp

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1ieee.org

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ams.org

mathscinet.ams.org

Drezner et al. (2002) Drezner, Zvi; Klamroth, Kathrin; Schöbel, Anita; Wesolowsky, George O. (2002). "The Weber problem". Facility Location: Applications and Theory. Springer, Berlin. pp. 1–36. ISBN 9783540213451. MR 1933966.
Krarup & Vajda (1997). Krarup, Jakob; Vajda, Steven (1997). "On Torricelli's geometrical solution to a problem of Fermat". IMA Journal of Mathematics Applied in Business and Industry. 8 (3): 215–224. doi:10.1093/imaman/8.3.215. MR 1473041.
Spain (1996). Spain, P. G. (1996). "The Fermat point of a triangle". Mathematics Magazine. 69 (2): 131–133. doi:10.1080/0025570X.1996.11996409. JSTOR 2690672?origin=pubexport. MR 1573157.
Brimberg (1995). Brimberg, J. (1995). "The Fermat–Weber location problem revisited". Mathematical Programming. 71 (1, Ser. A): 71–76. doi:10.1007/BF01592245. MR 1362958. S2CID 206800756.
Vardi & Zhang (2000) Vardi, Yehuda; Zhang, Cun-Hui (2000). "The multivariate $L 1$ -median and associated data depth". Proceedings of the National Academy of Sciences of the United States of America. 97 (4): 1423–1426 (electronic). Bibcode:2000PNAS...97.1423V. doi:10.1073/pnas.97.4.1423. MR 1740461. PMC 26449. PMID 10677477.

books.google.com

Drezner et al. (2002) Drezner, Zvi; Klamroth, Kathrin; Schöbel, Anita; Wesolowsky, George O. (2002). "The Weber problem". Facility Location: Applications and Theory. Springer, Berlin. pp. 1–36. ISBN 9783540213451. MR 1933966.
Cieslik (2006). Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394.
Eiselt & Marianov (2011). Eiselt, H. A.; Marianov, Vladimir (2011). Foundations of Location Analysis. International Series in Operations Research & Management Science. Vol. 155. Springer. p. 6. ISBN 9781441975720.
Cieslik (2006), p. 6; Plastria (2006). The convex case was originally proven by Giovanni Fagnano. Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394. Plastria, Frank (2006). "Four-point Fermat location problems revisited. New proofs and extensions of old results" (PDF). IMA Journal of Management Mathematics. 17 (4): 387–396. doi:10.1093/imaman/dpl007. Zbl 1126.90046. Archived from the original (PDF) on 2016-03-04. Retrieved 2014-05-18..

carleton.ca

scs.carleton.ca

Bose, Maheshwari & Morin (2003). Bose, Prosenjit; Maheshwari, Anil; Morin, Pat (2003). "Fast approximations for sums of distances, clustering and the Fermat–Weber problem". Computational Geometry: Theory and Applications. 24 (3): 135–146. doi:10.1016/S0925-7721(02)00102-5.

doi.org

Dodge & Rousson (1999). Dodge, Yadolah; Rousson, Valentin (September 1999). "Multivariate $L 1$ mean". Metrika. 49 (2): 127–134. doi:10.1007/s001840050029.
Krarup & Vajda (1997). Krarup, Jakob; Vajda, Steven (1997). "On Torricelli's geometrical solution to a problem of Fermat". IMA Journal of Mathematics Applied in Business and Industry. 8 (3): 215–224. doi:10.1093/imaman/8.3.215. MR 1473041.
Spain (1996). Spain, P. G. (1996). "The Fermat point of a triangle". Mathematics Magazine. 69 (2): 131–133. doi:10.1080/0025570X.1996.11996409. JSTOR 2690672?origin=pubexport. MR 1573157.
Brimberg (1995). Brimberg, J. (1995). "The Fermat–Weber location problem revisited". Mathematical Programming. 71 (1, Ser. A): 71–76. doi:10.1007/BF01592245. MR 1362958. S2CID 206800756.
Bose, Maheshwari & Morin (2003). Bose, Prosenjit; Maheshwari, Anil; Morin, Pat (2003). "Fast approximations for sums of distances, clustering and the Fermat–Weber problem". Computational Geometry: Theory and Applications. 24 (3): 135–146. doi:10.1016/S0925-7721(02)00102-5.
Haldane (1948) Haldane, J. B. S. (1948). "Note on the median of a multivariate distribution". Biometrika. 35 (3–4): 414–417. doi:10.1093/biomet/35.3-4.414.
Vardi & Zhang (2000) Vardi, Yehuda; Zhang, Cun-Hui (2000). "The multivariate $L 1$ -median and associated data depth". Proceedings of the National Academy of Sciences of the United States of America. 97 (4): 1423–1426 (electronic). Bibcode:2000PNAS...97.1423V. doi:10.1073/pnas.97.4.1423. MR 1740461. PMC 26449. PMID 10677477.
Lopuhaä & Rousseeuw (1991) Lopuhaä, Hendrick P.; Rousseeuw, Peter J. (1991). "Breakdown points of affine equivariant estimators of multivariate location and covariance matrices". Annals of Statistics. 19 (1): 229–248. doi:10.1214/aos/1176347978. JSTOR 2241852.
Cieslik (2006), p. 6; Plastria (2006). The convex case was originally proven by Giovanni Fagnano. Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394. Plastria, Frank (2006). "Four-point Fermat location problems revisited. New proofs and extensions of old results" (PDF). IMA Journal of Management Mathematics. 17 (4): 387–396. doi:10.1093/imaman/dpl007. Zbl 1126.90046. Archived from the original (PDF) on 2016-03-04. Retrieved 2014-05-18..
Bajaj (1986); Bajaj (1988). Earlier, Cockayne & Melzak (1969) proved that the Steiner point for 5 points in the plane cannot be constructed with ruler and compass Bajaj, Chanderjit (1986). "Proving geometric algorithms nonsolvability: An application of factoring polynomials". Journal of Symbolic Computation. 2: 99–102. doi:10.1016/S0747-7171(86)80015-3. Bajaj, Chanderjit (1988). "The algebraic degree of geometric optimization problems". Discrete & Computational Geometry. 3 (2): 177–191. doi:10.1007/BF02187906. Cockayne, E. J.; Melzak, Z. A. (1969). "Euclidean constructability in graph minimization problems". Mathematics Magazine. 42 (4): 206–208. doi:10.2307/2688541. JSTOR 2688541.
Weiszfeld (1937); Kuhn (1973); Chandrasekaran & Tamir (1989). Weiszfeld, E. (1937). "Sur le point pour lequel la somme des distances de $n$ points donnes est minimum". Tohoku Mathematical Journal (in French). 43: 355–386. Translated into English as Weiszfeld, E.; Plastria, Frank (April 2008). "On the point for which the sum of the distances to $n$ given points is minimum". Annals of Operations Research. 167 (1): 7–41. doi:10.1007/s10479-008-0352-z. S2CID 21000317. Kuhn, Harold W. (1973). "A note on Fermat's problem". Mathematical Programming. 4 (1): 98–107. doi:10.1007/BF01584648. S2CID 22534094. Chandrasekaran, R.; Tamir, A. (1989). "Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem". Mathematical Programming. Series A. 44 (1–3): 293–295. doi:10.1007/BF01587094. S2CID 43224801.
Fletcher, Venkatasubramanian & Joshi (2009). Fletcher, P. Thomas; Venkatasubramanian, Suresh; Joshi, Sarang (2009). "The geometric median on Riemannian manifolds with application to robust atlas estimation". NeuroImage. 45 (1 Suppl): s143–s152. doi:10.1016/j.neuroimage.2008.10.052. PMC 2735114. PMID 19056498.

dtic.mil

apps.dtic.mil

Lawera & Thompson (1993). Lawera, Martin; Thompson, James R. (1993). "Some problems of estimation and testing in multivariate statistical process control" (PDF). Proceedings of the 38th Conference on the Design of Experiments. U.S. Army Research Office Report. Vol. 93–2. pp. 99–126. Archived from the original on May 17, 2014.

harvard.edu

ui.adsabs.harvard.edu

Vardi & Zhang (2000) Vardi, Yehuda; Zhang, Cun-Hui (2000). "The multivariate $L 1$ -median and associated data depth". Proceedings of the National Academy of Sciences of the United States of America. 97 (4): 1423–1426 (electronic). Bibcode:2000PNAS...97.1423V. doi:10.1073/pnas.97.4.1423. MR 1740461. PMC 26449. PMID 10677477.

ieee.org

ieeexplore.ieee.org

Fletcher, P. Thomas; Venkatasubramanian, Suresh; Joshi, Sarang (23 June 2008). "Robust statistics on Riemannian manifolds via the geometric median". 2008 IEEE Conference on Computer Vision and Pattern Recognition. IEEE Conference on Computer Vision and Pattern Recognition. Anchorage, AK, USA: IEEE.

jst.go.jp

jstage.jst.go.jp

Weiszfeld (1937); Kuhn (1973); Chandrasekaran & Tamir (1989). Weiszfeld, E. (1937). "Sur le point pour lequel la somme des distances de $n$ points donnes est minimum". Tohoku Mathematical Journal (in French). 43: 355–386. Translated into English as Weiszfeld, E.; Plastria, Frank (April 2008). "On the point for which the sum of the distances to $n$ given points is minimum". Annals of Operations Research. 167 (1): 7–41. doi:10.1007/s10479-008-0352-z. S2CID 21000317. Kuhn, Harold W. (1973). "A note on Fermat's problem". Mathematical Programming. 4 (1): 98–107. doi:10.1007/BF01584648. S2CID 22534094. Chandrasekaran, R.; Tamir, A. (1989). "Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem". Mathematical Programming. Series A. 44 (1–3): 293–295. doi:10.1007/BF01587094. S2CID 43224801.

jstor.org

Spain (1996). Spain, P. G. (1996). "The Fermat point of a triangle". Mathematics Magazine. 69 (2): 131–133. doi:10.1080/0025570X.1996.11996409. JSTOR 2690672?origin=pubexport. MR 1573157.
Lopuhaä & Rousseeuw (1991) Lopuhaä, Hendrick P.; Rousseeuw, Peter J. (1991). "Breakdown points of affine equivariant estimators of multivariate location and covariance matrices". Annals of Statistics. 19 (1): 229–248. doi:10.1214/aos/1176347978. JSTOR 2241852.
Bajaj (1986); Bajaj (1988). Earlier, Cockayne & Melzak (1969) proved that the Steiner point for 5 points in the plane cannot be constructed with ruler and compass Bajaj, Chanderjit (1986). "Proving geometric algorithms nonsolvability: An application of factoring polynomials". Journal of Symbolic Computation. 2: 99–102. doi:10.1016/S0747-7171(86)80015-3. Bajaj, Chanderjit (1988). "The algebraic degree of geometric optimization problems". Discrete & Computational Geometry. 3 (2): 177–191. doi:10.1007/BF02187906. Cockayne, E. J.; Melzak, Z. A. (1969). "Euclidean constructability in graph minimization problems". Mathematics Magazine. 42 (4): 206–208. doi:10.2307/2688541. JSTOR 2688541.

nih.gov

ncbi.nlm.nih.gov

Vardi & Zhang (2000) Vardi, Yehuda; Zhang, Cun-Hui (2000). "The multivariate $L 1$ -median and associated data depth". Proceedings of the National Academy of Sciences of the United States of America. 97 (4): 1423–1426 (electronic). Bibcode:2000PNAS...97.1423V. doi:10.1073/pnas.97.4.1423. MR 1740461. PMC 26449. PMID 10677477.
Fletcher, Venkatasubramanian & Joshi (2009). Fletcher, P. Thomas; Venkatasubramanian, Suresh; Joshi, Sarang (2009). "The geometric median on Riemannian manifolds with application to robust atlas estimation". NeuroImage. 45 (1 Suppl): s143–s152. doi:10.1016/j.neuroimage.2008.10.052. PMC 2735114. PMID 19056498.

pubmed.ncbi.nlm.nih.gov

Vardi & Zhang (2000) Vardi, Yehuda; Zhang, Cun-Hui (2000). "The multivariate $L 1$ -median and associated data depth". Proceedings of the National Academy of Sciences of the United States of America. 97 (4): 1423–1426 (electronic). Bibcode:2000PNAS...97.1423V. doi:10.1073/pnas.97.4.1423. MR 1740461. PMC 26449. PMID 10677477.
Fletcher, Venkatasubramanian & Joshi (2009). Fletcher, P. Thomas; Venkatasubramanian, Suresh; Joshi, Sarang (2009). "The geometric median on Riemannian manifolds with application to robust atlas estimation". NeuroImage. 45 (1 Suppl): s143–s152. doi:10.1016/j.neuroimage.2008.10.052. PMC 2735114. PMID 19056498.

purdue.edu

docs.lib.purdue.edu

Bajaj (1986); Bajaj (1988). Earlier, Cockayne & Melzak (1969) proved that the Steiner point for 5 points in the plane cannot be constructed with ruler and compass Bajaj, Chanderjit (1986). "Proving geometric algorithms nonsolvability: An application of factoring polynomials". Journal of Symbolic Computation. 2: 99–102. doi:10.1016/S0747-7171(86)80015-3. Bajaj, Chanderjit (1988). "The algebraic degree of geometric optimization problems". Discrete & Computational Geometry. 3 (2): 177–191. doi:10.1007/BF02187906. Cockayne, E. J.; Melzak, Z. A. (1969). "Euclidean constructability in graph minimization problems". Mathematics Magazine. 42 (4): 206–208. doi:10.2307/2688541. JSTOR 2688541.

semanticscholar.org

api.semanticscholar.org

Brimberg (1995). Brimberg, J. (1995). "The Fermat–Weber location problem revisited". Mathematical Programming. 71 (1, Ser. A): 71–76. doi:10.1007/BF01592245. MR 1362958. S2CID 206800756.
Weiszfeld (1937); Kuhn (1973); Chandrasekaran & Tamir (1989). Weiszfeld, E. (1937). "Sur le point pour lequel la somme des distances de $n$ points donnes est minimum". Tohoku Mathematical Journal (in French). 43: 355–386. Translated into English as Weiszfeld, E.; Plastria, Frank (April 2008). "On the point for which the sum of the distances to $n$ given points is minimum". Annals of Operations Research. 167 (1): 7–41. doi:10.1007/s10479-008-0352-z. S2CID 21000317. Kuhn, Harold W. (1973). "A note on Fermat's problem". Mathematical Programming. 4 (1): 98–107. doi:10.1007/BF01584648. S2CID 22534094. Chandrasekaran, R.; Tamir, A. (1989). "Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem". Mathematical Programming. Series A. 44 (1–3): 293–295. doi:10.1007/BF01587094. S2CID 43224801.

tudelft.nl

repository.tudelft.nl

Lopuhaä & Rousseeuw (1991) Lopuhaä, Hendrick P.; Rousseeuw, Peter J. (1991). "Breakdown points of affine equivariant estimators of multivariate location and covariance matrices". Annals of Statistics. 19 (1): 229–248. doi:10.1214/aos/1176347978. JSTOR 2241852.

vub.ac.be

mosi.vub.ac.be

Cieslik (2006), p. 6; Plastria (2006). The convex case was originally proven by Giovanni Fagnano. Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394. Plastria, Frank (2006). "Four-point Fermat location problems revisited. New proofs and extensions of old results" (PDF). IMA Journal of Management Mathematics. 17 (4): 387–396. doi:10.1093/imaman/dpl007. Zbl 1126.90046. Archived from the original (PDF) on 2016-03-04. Retrieved 2014-05-18..

web.archive.org

Lawera & Thompson (1993). Lawera, Martin; Thompson, James R. (1993). "Some problems of estimation and testing in multivariate statistical process control" (PDF). Proceedings of the 38th Conference on the Design of Experiments. U.S. Army Research Office Report. Vol. 93–2. pp. 99–126. Archived from the original on May 17, 2014.
Cieslik (2006), p. 6; Plastria (2006). The convex case was originally proven by Giovanni Fagnano. Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394. Plastria, Frank (2006). "Four-point Fermat location problems revisited. New proofs and extensions of old results" (PDF). IMA Journal of Management Mathematics. 17 (4): 387–396. doi:10.1093/imaman/dpl007. Zbl 1126.90046. Archived from the original (PDF) on 2016-03-04. Retrieved 2014-05-18..

zbmath.org

Cieslik (2006), p. 6; Plastria (2006). The convex case was originally proven by Giovanni Fagnano. Cieslik, Dietmar (2006). Shortest Connectivity: An Introduction with Applications in Phylogeny. Combinatorial Optimization. Vol. 17. Springer. p. 3. ISBN 9780387235394. Plastria, Frank (2006). "Four-point Fermat location problems revisited. New proofs and extensions of old results" (PDF). IMA Journal of Management Mathematics. 17 (4): 387–396. doi:10.1093/imaman/dpl007. Zbl 1126.90046. Archived from the original (PDF) on 2016-03-04. Retrieved 2014-05-18..