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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.
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Submitted on : Thursday, January 19, 2012 - 4:29:40 PM
Last modification on : Tuesday, October 19, 2021 - 11:58:53 PM
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  • HAL Id : hal-00661473, version 1


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



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