Finite Unordered Set
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A Finite Unordered Set is an ordered set that is a finite set.
- AKA: Nominal Scale.
- …
- Example(s):
- a Categorical Set.
- …
- Counter-Example(s):
- See: Unordered Multiset, Finite Multiset, Ratio Scale, Interval Scale.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Level_of_measurement#Nominal_scale Retrieved:2015-6-1.
- The nominal type differentiates between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to; thus dichotomous data involves the construction of classifications as well as the classification of items. Discovery of an exception to a classification can be viewed as progress. Numbers may be used to represent the variables but the numbers do not have numerical value or relationship.
Examples of these classifications include gender, nationality, ethnicity, language, genre, style, biological species, and form.[1][2] In a university one could also use hall of affiliation as an example. Other concrete examples are
- in grammar, the parts of speech: noun, verb, preposition, article, pronoun, etc.
- in politics, power projection: hard power, soft power, etc.
- in biology, the taxonomic ranks below domains: Archaea, Bacteria, and Eukarya
- Nominal scales were often called qualitative scales, and measurements made on qualitative scales were called qualitative data. However, the rise of qualitative research has made this usage confusing.
- The nominal type differentiates between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to; thus dichotomous data involves the construction of classifications as well as the classification of items. Discovery of an exception to a classification can be viewed as progress. Numbers may be used to represent the variables but the numbers do not have numerical value or relationship.
- ↑ Nominal measures are based on sets and depend on categories, ala Aristotle. accessdate=2014-08-25
- ↑ "Invariably one came up against fundamental physical limits to the accuracy of measurement. … The art of physical measurement seemed to be a matter of compromise, of choosing between reciprocally related uncertainties. … Multiplying together the conjugate pairs of uncertainty limits mentioned, however, I found that they formed invariant products of not one but two distinct kinds. … The first group of limits were calculable a priori from a specification of the instrument. The second group could be calculated only a posteriori from a specification of what was done with the instrument. … In the first case each unit [of information] would add one additional dimension (conceptual category), whereas in the second each unit would add one additional atomic fact.", – pp. 1–4: MacKay, Donald M. (1969), Information, Mechanism, and Meaning, Cambridge, MA: MIT Press, ISBN 0-262-63-032-X
1999
- (Herbrich et al., 1999) ⇒ Ralf Herbrich, Thore Graepel, and Klaus Obermayer. (1999). “Support Vector Learning for Ordinal Regression.” In: Proceedings of the Ninth International Conference on Artificial Neural Networks.
- QUOTE: Two main scenarios were considered in the past: (i) If [math]\displaystyle{ Y }[/math] is a finite unordered set (nominal scale), the task is referred to as classification. Since Y is unordered, the 0-1 loss,