Geodesic
Computational complexity of two problems of~cognitive~data~analysis
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 1, pp. 18-32

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The NP-hardness in the strong sense is proved for two problems of cognitive data analysis. One of them is the problem of taxonomy (clustering), i. e. splitting an unclassified sample of objects into disjoint subsets. The other is the problem of sampling a subset of typical representatives of a classified sample which consists of objects of two images. The first problem can be considered as a special case of the second problem, provided that one of the images consists of one object. To obtain a quantitative quality estimate for the set of selected typical representatives of the sample, the function of rival similarity (FRiS function) is used, which assesses the similarity of an object with the closest typical object. Illustr. 1, bibliogr. 18.
Keywords: NP-hardness, taxonomy (clustering), typical object (prototypes) selection, function of rival similarity. 
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O. A. Kutnenko. Computational complexity of two problems of~cognitive~data~analysis. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 1, pp. 18-32. http://geodesic.mathdoc.fr/item/DA_2022_29_1_a1/