## 15. ÖMG-Kongress

Jahrestagung der Deutschen Mathematikervereinigung

#### 16. bis 22. September 2001 in Wien

**Sektion 12 - Wahrscheinlichkeitstheorie, Statistik**

Montag, 17. September 2001, 18.30, Hörsaal 7

**Numerical Taxonomy Methods for Statistical Data Processing**
**Tiberiu Postelnicu**, **Rumänische Akademie**

The purpose of numerical taxonomy can be briefly defined as the construction of objective clusters of units by means of a quantitative measure of their affinity. Its name comes from the fact that the first methods were proposed for, and essentially applied to, the biological classification.

Numerical taxonomy methods present a very powerful multiple comparison instrument. More general, cluster analysis is the name given to various procedures whereby a set of individuals or units, termed as ``Operational Taxonomic Units'' (OTU). Techniques of cluster analysis can be applied in different fields of medicine: the recognition of various clinical forms of a disease, separation of distinctive racial groups, treatment of quantitative biogeographical data, etc.

An important case for statistical data processing deals with OTUs described by binary attributes. Homogeneities for binary and for ordered multistates data are presented. Methods of automatic classification are described and two types of homogeneities for the classification in biology and the genetics of the human populations are given.

The new extension concerns the inference in contingency table and it is applicable in any field. The connection between numerical taxonomy, one side, and the cluster analysis, as well as the discriminant analysis, on the other side, is useful to be considered.

[1] |
Dragomirescu L., Postelnicu T., (1994), Specific numerical taxonomy methods in biological classification. In ``Statistical Tools in Human Biology''., World Scientific, 31-46. |

[2] |
Buser M.W., Baroni-Urbani C., (1982), A direct nondimensional clustering method for binary data. Biometrics, 38, 351-360. |

[3] |
Sneath P.H.A., Sokal R.R., (1973), Numerical taxonomy. San Francisco Freeman. |

[4] |
Vichi,M. (1998), Principal classification analysis: a method for generating consensus dendrograms and its application to three way data. Computational Statistics & Data Analysis, 27, 3, 311-331. |

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