title: A probabilistic approach to comparing the distances between partitions of a set
metadata.name: dc.contributor.author
metadata.value: Rogov, Aleksandr A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Varfolomeyev, Aleksey G.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Timonin, Artem O.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Proen¸ca, Kseniya A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-05T09:01:05Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-05T09:01:05Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Rogov A. A., Varfolomeyev A. G., Timonin A. O., Proen¸ca K. A. A probabilistic approach to comparing the distances between partitions of a set. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 1, pp. 14–19.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2018.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9322
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This article describes and compares a number of classical metrics to compare different
  approaches to partition a given set, such as the Rand index, the Larsen and Aone coefficient,
  among others. We developed a probabilistic framework to compare these metrics and unified
  representation of distances that uses a common set of parameters. This is done by taking all
  possible values of similarity measurements between different possible partitions and graduating
  them by using quantiles of a distribution function. Let λα be a quantile with α level for
  distribution function Fρ (t) = P (ρ < t). Then if the proximity measurement ρ is not less than
  λα, we can conclude that α · 100% of randomly chosen pairs of partitions have a proximity
  measurement less than ρ. This means that these partitions can neither be considered close nor
  similar. This paper identifies the general case of distribution functions that describe similarity
  measurements, with a special focus on uniform distributions. The comparison results are
  presented in tables for quantiles of probability distributions, using computer simulations over
  our selected set of similarity metrics. Refs 9. Table 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work was supported by the Program of Strategic Development of Retrozavodsk State University
  within the framework of the implementation of a set of activities for the development of research activities
  for 2012–2016.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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 14; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: distance between partitions of a set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: probabilistic approach
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: comparing the distances
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A probabilistic approach to comparing the distances between partitions of a set
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02-Rogov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9322/1/02-Rogov.pdf
resources.format: Adobe PDF
resources.size: 231,56 kB