Eigenanalysis and metric multidimensional scaling on hierarchical structures.

Carles Maria Cuadras; Josep-Maria Oller

Qüestiió (1987)

  • Volume: 11, Issue: 3, page 37-57
  • ISSN: 0210-8054

Abstract

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The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing compact clusters and representing objects inside every cluster.

How to cite

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Cuadras, Carles Maria, and Oller, Josep-Maria. "Eigenanalysis and metric multidimensional scaling on hierarchical structures.." Qüestiió 11.3 (1987): 37-57. <http://eudml.org/doc/40122>.

@article{Cuadras1987,
abstract = {The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing compact clusters and representing objects inside every cluster.},
author = {Cuadras, Carles Maria, Oller, Josep-Maria},
journal = {Qüestiió},
keywords = {Análisis cluster; Distancias ultramétricas; Autovalores; Coordenadas; ultrametric tree; clustering; principal coordinate analysis; latent vectors; proximity data; Euclidean space},
language = {eng},
number = {3},
pages = {37-57},
title = {Eigenanalysis and metric multidimensional scaling on hierarchical structures.},
url = {http://eudml.org/doc/40122},
volume = {11},
year = {1987},
}

TY - JOUR
AU - Cuadras, Carles Maria
AU - Oller, Josep-Maria
TI - Eigenanalysis and metric multidimensional scaling on hierarchical structures.
JO - Qüestiió
PY - 1987
VL - 11
IS - 3
SP - 37
EP - 57
AB - The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing compact clusters and representing objects inside every cluster.
LA - eng
KW - Análisis cluster; Distancias ultramétricas; Autovalores; Coordenadas; ultrametric tree; clustering; principal coordinate analysis; latent vectors; proximity data; Euclidean space
UR - http://eudml.org/doc/40122
ER -

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