Skip to Main content Skip to Navigation
Journal articles

Evidential reasoning in large partially ordered sets. Application to multi-label classification, ensemble clustering and preference aggregation

Abstract : The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment Omega are usually defined in the power set 2^Omega, resulting in exponential complexity of the operations involved in this framework, such as combination rules. When Omega is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as the power set, the set of partitions, or the set of preorders of a finite set. Applications to multi-label classification, ensemble clustering and preference aggregation are demonstrated.
Document type :
Journal articles
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00684520
Contributor : Thierry Denoeux <>
Submitted on : Monday, April 2, 2012 - 12:59:56 PM
Last modification on : Tuesday, March 17, 2020 - 10:45:17 AM
Document(s) archivé(s) le : Tuesday, July 3, 2012 - 2:32:12 AM

File

aor2011.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00684520, version 1

Collections

Citation

Thierry Denoeux, Marie-Hélène Masson. Evidential reasoning in large partially ordered sets. Application to multi-label classification, ensemble clustering and preference aggregation. Annals of Operations Research, Springer Verlag, 2012, 195 (1), pp.135-161. ⟨hal-00684520⟩

Share

Metrics

Record views

252

Files downloads

168