Facets of the set theoretic representation of categorical data

Abstract : There are three basic notions in Data Analysis : object, category and descriptive attribute. Two description cases are of concern ; describing an object set O or describing a category set C. For the former case the set theoretic representation of a given attribute is defined with respect to O and for the latter, it is defined within each category of C. For these representations a given descriptive attribute is interpreted in terms of a relation with a given arity defined on the described set. We propose in this work a unique principle for the set theoretic representation of a descriptive attribute of different types : boolean, numerical, nominal categorical, ordinal categorical, preordonance categorical, taxonomic categorical and taxonomic preordonance categorical. The formal representations of these different types are explicited and compared in both cases : for an object set description and for a category set description. Then these representations are applied in interesting real examples.
Document type :
Reports
Liste complète des métadonnées

Cited literature [45 references]  Display  Hide  Download

https://hal.inria.fr/hal-00661473
Contributor : Ist Rennes <>
Submitted on : Thursday, January 19, 2012 - 4:29:40 PM
Last modification on : Thursday, November 15, 2018 - 11:57:44 AM
Document(s) archivé(s) le : Monday, November 19, 2012 - 2:05:08 PM

File

PI-1988.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00661473, version 1

Citation

Israël-César Lerman. Facets of the set theoretic representation of categorical data. [Research Report] PI-1988, 2012, pp.34. ⟨hal-00661473⟩

Share

Metrics

Record views

187

Files downloads

76