On the Axiomatization of Generalized Entropic Metrics

Simovici, Dan A.

doi:10.1109/ismvl.2007.40

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 4 Let P Be a Partition Of U Then Normalized Disc(p1

Definition1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gini index is a special case of the general entropy of partitions discussed in Simovici (2007), which conforms to an axiom system proposed for possible entropy measures. A natural question is whether the normalized disconnectivity can fit into the axiom system by extending those axioms to covers.…”

Section: Theorem 4 Let P Be a Partition Of U Then Normalized Disc(pmentioning

confidence: 87%

See 1 more Smart Citation

Entropy on covers

Wang

2011

Data Min Knowl Disc

View full text Add to dashboard Cite

As a generalization of partitions, covers allow overlaps between their members. In this paper, we will propose a family of entropy-like measures over covers, which are anti monotonic with regard to the partial order defined by refinement relations of covers. In parallel to the entropy theory, we also develop their conditional forms, which in turn lead to a family of semi-metrics on covers. These make it possible to apply entropy-based techniques in data mining or machine learning to problems naturally modelled by covers.

show abstract

Section: Theorem 4 Let P Be a Partition Of U Then Normalized Disc(pmentioning

confidence: 87%

“…2.2 Generalized entropy Simovici (2007), generalizes entropy on a partition to a family of measurements through the following axioms:…”

Section: Definitionmentioning

confidence: 99%