F. Cordellier and J.Ch. Giorot. On the Fermat-Weber Problem with Convex Cost Functionals. Mathematical Programming, 14:295--311, 1978. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Mathematical Programming Approaches To Machine Learning And Data.. - Bradley (1998) (1 citation) (Correct)
....clusters. We also note that the k Mean Algorithm 85 3.1. 4 finds a stationary point not of problem (54) but of the same problem with kD i k 2 replaced with kD i k 2 2 (53) Without the squared distance term, the subproblem of the k Mean algorithm becomes the considerably harder Weber problem [128, 45] which locates a center in R n closest in sum of Euclidean distances (not their squares) to a given finite set of points. The Weber problem has no closed form solution. However, using the mean as a center of points assigned to the cluster minimizes the sum of the squares of the distances from ....
F. Cordellier and J. Ch. Fiorot. On the Fermat-Weber problem with convex cost functionals. Mathematical Programming, 14:295--311, 1978.
The Newton Bracketing Method for Convex Minimization - Levin, Ben-Israel (2000) (Correct)
....A, where the weights (31) are undefined. The Weiszfeld method is the standard, and best known, method for solving the Fermat Weber location problem. The convergence of the Weiszfeld method was studied in [16] 13] and [6] Further references: ffl The Fermat Weber problem: 1] 3] 4] 7] [8], 9] 10] 11] 14] Page 12 RRR 33 2000 ffl The Weiszfeld method and generalizations: 5] 12] 18] 20] 21] 22] 23] 25] ffl Other methods: 19] 24] 27] We propose here an alternative method for the approximate solution of the Fermat Weber problem (28) Algorithm 2 with ....
F. Cordellier and J.Ch. Fiorot, On the Fermat--Weber problem with convex cost functions, Math. Prog. 14 (1978), 295--311
Clustering via Concave Minimization - Bradley, Mangasarian, Street (1997) (7 citations) (Correct)
....We also note that the k Mean Algorithm finds a stationary point not of problem (5) with p = 2, but of the same problem except that kD i k 2 is replaced by kD i k 2 2 . Without this squared distance term, the subproblem of the k Mean Algorithm becomes the considerably harder Weber problem [17, 5] which locates a center in R n closest in sum of Euclidean distances (not their squares ) to a finite set of given points. The Weber problem has no closed form solution. However, using the mean as a cluster center of points assigned to the cluster, minimizes the sum of the squares of the ....
F. Cordellier and J. Ch. Fiorot. On the Fermat-Weber problem with convex cost functionals. Mathematical Programming, 14:295--311, 1978.
Mathematical Programming in Data Mining - Mangasarian (1996) (18 citations) (Correct)
....k Mean Algorithm finds a stationary point not of problem (13) with p = 2, but of the same problem except that kD i k 2 is replaced by kD i k 2 2 and thus favoring outliers. Without this squared distance term, the subproblem of the k Mean Algorithm becomes the considerably harder Weber problem [56, 13] which locates a center in R n closest in sum of Euclidean distances (not their squares ) to a finite set of given points. The Weber problem has no closed form solution. However, using the mean as a cluster center of points assigned to the cluster, as done in the k Mean Algorithm, minimizes the ....
F. Cordellier and J. Ch. Fiorot. On the Fermat-Weber problem with convex cost functionals. Mathematical Programming, 14:295--311, 1978.
Mathematical Programming for Data Mining: Formulations.. - Bradley, Fayyad.. (1998) (9 citations) (Correct)
....center that minimizes the sum of the 2 norm distances squared to all the points in cluster . Stop when c ;j = c ;j 1 ; 1; k. If the 2 norm (not 2 norm squared) is used in the objective of (43) the cluster center update subproblem becomes the considerably harder Weber problem [38, 100] which locates a center in R n closest in sum of Euclidean distances to a finite set of given points. Choosing the mean of the points assigned to a given cluster as its center minimizes the sum of the 2 norm distances squared between the data points and the cluster center. This property makes ....
F. Cordellier and J. Ch. Fiorot. On the Fermat-Weber problem with convex cost functionals. Mathematical Programming, 14:295--311, 1978.
Models For Robust Estimation And Identification - Chandrasekaran Schubert.. (Correct)
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F. Cordellier and J.Ch. Giorot. On the Fermat-Weber Problem with Convex Cost Functionals. Mathematical Programming, 14:295--311, 1978.
Clustering via Concave Minimization - Bradley And Mangasarian (1997) (7 citations) (Correct)
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F. Cordellier and J. Ch. Fiorot. On the Fermat-Weber problem with convex cost functionals. Mathematical Programming, 14:295--311, 1978.
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