title: MDM method for solving the general quadratic problem of mathematical diagnostics
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vassili N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Solovyeva, Natalya A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-10-10T09:43:27Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-10-10T09:43:27Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V.N., Solovyeva N.A. MDM method for solving the general quadratic problem of mathematical diagnostics. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 3, pp. 516–529. https://doi.org/10.21638/spbu01.2023.306 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.306
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44173
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The term mathematical diagnostics was introduced by V. F.Demyanov in the early 2000s.
  The simplest problem of mathematical diagnostics is to determine the relative position of
  a certain point p and the convex hull C of a finite number of given points in n-dimensional
  Euclidean space. Of interest is the answer to the following questions: does the point p belong
  to the set C or not? If p does not belong to C, then what is the distance from p to C? In
  general problem of mathematical diagnostics two convex hulls are considered. The question
  is whether they have common points. If there are no common points, then it is required to
  find the distance between these hulls. From an algorithmic point of view, the problems of
  mathematical diagnostics are reduced to special problems of linear or quadratic programming,
  for the solution of which there are finite methods. However, when implementing this
  approach in the case of large data arrays, serious computational difficulties arise. Infinite
  but easily implemented methods come to the rescue, which allow obtaining an approximate
  solution with the required accuracy in a finite number of iterations. These methods include
  the MDM method. It was developed by Mitchell, Demyanov and Malozemov in 1971 for
  other purposes, but later found application in machine learning. From a modern point of
  view, the original version of the MDM method can be used to solve the simplest problems of
  mathematical diagnostics. This article gives a natural generalization of the MDM-method,
  oriented towards solving general problems of mathematical diagnostics. The equivalence of
  the general problem of mathematical diagnostics and the problem of linear separation of
  two finite sets with the largest width of the margin is established.
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 10 (68); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: mathematical diagnostics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: simplest problem of mathematical diagnostics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: general problem of mathematical diagnostics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: machine learning
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: MDM-algorithm
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: MDM method for solving the general quadratic problem of mathematical diagnostics
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 516-529.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44173/1/516-529.pdf
resources.format: Adobe PDF
resources.size: 309,99 kB