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Volume 29, No 1, 2022, P. 18-32
UDC 519.87+519.854
O. A. Kutnenko
Computational complexity of two problems of cognitive data analysis
Abstract:
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.
DOI: 10.33048/daio.2022.29.713
Olga A. Kutnenko 1,2
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: olga@math.nsc.ru
Received April 26, 2021
Revised December 2, 2021
Accepted December 3, 2021
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