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Variance and clustering
Author(s):
Yannis
G.
Yatracos
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1177-1179.
MSC (1991):
Primary 62H30, 62J10
MathSciNet review:
1458273
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Abstract:
A measure of dissimilarity of real observations is introduced that is used to identify clusters and is based on ``gaps'', and also on averages of selected subgroups of the observations. This measure is surprisingly associated with the sample variance in a way that leads to a new identity and interpretation of the notion of variance.
References:
- 1.
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- 2.
- Block, H. and Fang, Z.(1988) A multivariate extension of Hoeffding's Lemma. Ann. Probab. 16, 1803-1821. MR 90a:62133
- 3.
- Hoeffding, W.(1940) Masstabinvariante Korrelationstheorie. Schr. Math. Inst. Univ. Berlin 5, 181-223.
- 4.
- Johnson, R.A. and Wichern, D.W.(1988) Applied Multivariate Statistical Analysis. 2nd ed., Prentice-Hall, New Jersey. MR 84a:62086 (1st ed.)
- 5.
- Pearson, K.(1926) On the coefficient of racial likeness. Biometrika 18, 105-117.
- 6.
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- 7.
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- 8.
- Tukey, J. W.(1949) Comparing individual means in the analysis of variance. Biometrics 5, 99-114. MR 11:43c
- 9.
- Yatracos, Y. G.(1997) Variance, clustering and identification of high leverage points. Tech. Report STT 97-1, Dept. of Mathematics and Statistics, Univ. of Montreal.
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Additional Information:
Yannis
G.
Yatracos
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP 6128, Suc. Centre Ville, Montréal, Canada H3C 3J7
Email:
yatracos@dms.umontreal.ca
DOI:
10.1090/S0002-9939-98-04524-9
PII:
S 0002-9939(98)04524-9
Keywords:
Clustering,
divergence of populations,
analysis of variance
Received by editor(s):
October 4, 1996
Communicated by:
Wei Y. Loh
Copyright of article:
Copyright
1998,
American Mathematical Society
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