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Alternatives for Greedy Discrete Subsampling: Various Approaches Including Cluster Subsampling of COVID-19 Data With No Response Variable

Štěpánek Lubomír, Habarta Filip, Malá Ivana, Marek Luboš

Annals of Computer Science and Information Systems

2021

Vol. 26

103--111

An exhaustive selection of all possible combinations of n = 400 from N = 698 observations of the COVID-19 dataset was used as a benchmark. Building a random set of subsamples and choosing the one that minimized an averaged sum of squares of each variable's category frequency returned similar results as a "forward" subselection reducing the dataset one-by-one observation by the same metric's permanent lowering. That works similarly as k-means clustering (with a random clusters' number) over the original dataset's observations and choosing a subsample from each cluster proportionally to its size. However, the approaches differ significantly in asymptotic time complexity.

Type-reduction of the discretised interval type-2 fuzzy set : approaching the continuous case through progressively finer discretisation

Greenfield S., Chiclana F.

Journal of Artificial Intelligence and Soft Computing Research

2011

Vol. 1, No. 3

183--193

The defuzzification of a type-2 fuzzy set is a two stage process consisting of firstly type-reduction, and secondly defuzzification of the resultant type-1 set. This paper considers three approaches to discrete interval type-reduction: 1. The exhaustive method which produces the Type-Reduced Set, 2. the Greenfield-Chiclana Collapsing Defuzzifier which gives rise to the Representative Embedded Set Approximation, and 3. the Nie-Tan Method from which the Nie-Tan Set is derived. In the discrete case these three type-1 sets are distinct. The behavior of the three sets under fine discretisation is investigated experimentally, in order to shed light on the relationships between the continuous versions of these type-1 sets.