title: Approximate factorization of positive matrices by using methods of tropical optimization
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Romanova, Elizaveta Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-01-19T13:03:04Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-01-19T13:03:04Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N. K., Romanova E. Yu. Approximate factorization of positive matrices by using methods of tropical optimization. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 4, pp. 357–374.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.402
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/22452
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of rank-one factorization of positive matrices with missing (unspecified) entries
  is considered where a matrix is approximated by a product of column and row vectors that
  are subject to box constraints. The problem is reduced to the constrained approximation
  of the matrix, using the Chebyshev metric in logarithmic scale, by a matrix of unit rank.
  Furthermore, the approximation problem is formulated in terms of tropical mathematics
  that deals with the theory and applications of algebraic systems with idempotent addition.
  By using methods of tropical optimization, direct analytical solutions to the problem are
  derived for the case of an arbitrary positive matrix and for the case when the matrix does
  not contain columns (rows) with all entries missing. The results obtained allow one to find the
  vectors of the factor decomposition by using expressions in a parametric form which is ready
  for further analysis and immediate calculation. In conclusion, an example of approximate
  rank-one factorization of a matrix with missing entries is provided.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Research (grant N 20-010-00145).
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. Applied Mathematics. Computer Science. Control Processes;Volume 16; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: positive matrix factorization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rank-one matrix approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: log-Chebyshev distance function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: max-algebra
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Approximate factorization of positive matrices by using methods of tropical optimization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 357-374.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/22452/1/357-374.pdf
resources.format: Adobe PDF
resources.size: 302,7 kB