title: The symptom-syndrome analysis of multivariate categorical data based on Zhegalkin polynomials
metadata.name: dc.contributor.author
metadata.value: Alekseeva, Nina P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-10-07T11:35:53Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-10-07T11:35:53Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Alekseeva N.P. The symptom-syndrome analysis of multivariate categorical data based on Zhegalkin polynomials. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 3, pp. 394–405.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33256
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this article, we study the distribution, entropy and other informational properties of finite projective subspaces (syndromes) parameterized by impulse sequences with basic elements in the form of symptoms – polynomials over the field F2 which are known as Zhegalkin polynomials. It has been proven that the super syndrome, which is a linear syndrome with basic elements in the form of a multiplicative syndrome, is closed. If in the multiplication of two symptoms one is neutral, then we are talking about its majorization. The ordered by majorization symptoms form a majorized syndrome. Is proved that the majorized syndrome is closed and coincides with the super syndrome. The statements formulated in the first part of the paper are used to justify the convergence of the iterative procedure (PI), in which the most informative symptoms selected from partial super syndromes are again used in the next step. The stationary state of PI is obtained if all elements of the input set belong to either the same partial super syndrome or to the majorized syndrome. Thanks IP it is possible to quickly find the optimal syndrome from a large set of variables. An example from phthisiology shows how the specificity of classification can be improved using symptom analysis.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Foundation for Basic Research (grant No. 20-01-00096-а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: multivariate analysis of categorical data
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: finite geometries
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: algebraic normal forms
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: entropy
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uncertainty coefficient
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: iterative procedure
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: symptom-syndromic method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dimension reduction
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: classification
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: sensitivity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: specificity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The symptom-syndrome analysis of multivariate categorical data based on Zhegalkin polynomials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 394-405.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33256/1/394-405.pdf
resources.format: Adobe PDF
resources.size: 360,57 kB