by Francis Caillez, Pascale Kuntz
Abstract:
This paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their Euclidean nature. We present several particular transformations which preserve Euclideanarity and we complete, through the study of a one-parameter family, the current knowledge of the metric and Euclidean structure of coefficients based on binary data. These results are directly deduced from two theorems which prove the positive semi-definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used.
Reference:
A contribution to the study of the metric and Euclidean structures of dissimilarities (Francis Caillez, Pascale Kuntz), In Psychometrika, Springer New York, volume 61, 1996.
Bibtex Entry:
@article{Caillez1996,
abstract = {This paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their Euclidean nature. We present several particular transformations which preserve Euclideanarity and we complete, through the study of a one-parameter family, the current knowledge of the metric and Euclidean structure of coefficients based on binary data. These results are directly deduced from two theorems which prove the positive semi-definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used.},
author = {Caillez, Francis and Kuntz, Pascale},
doi = {10.1007/BF02294337},
issn = {0033-3123},
journal = {Psychometrika},
keywords = {Humanities,SML-LIB-BIBLIO,Social Sciences and Law,lang:ENG},
mendeley-tags = {SML-LIB-BIBLIO,lang:ENG},
month = jun,
number = {2},
pages = {241--253},
publisher = {Springer New York},
title = {{A contribution to the study of the metric and Euclidean structures of dissimilarities}},
url = {http://www.springerlink.com/content/f43471v55l716l48/},
volume = {61},
year = {1996}
}