Paper Info
Title
The graph-theoretical properties of partitions and information entropy
Abstract
The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoretical properties. Given a non-empty universe U, all the partitions G on U are taken as nodes, and a relation V between partitions are defined and taken as edges. The graph obtained is denoted by (G,V), which represents the connections between partitions on U. According to the values of the information entropy of partitions, a directed graph $(G,\overrightarrow{V})$ is defined on (G,V). It will be proved that there is a set of partitions with the minimal entropy; and a set of partitions with the maximal entropy; and the entropy is non-decreasing on any directed pathes in $(G,\overrightarrow{V})$ from a partition with the minimal entropy to one of the partitions with the maximal entropy. Hence, in $(G,\overrightarrow{V})$ the information entropy of partitions is represented in a clearly structured way.
Year
DOI
Venue
2005
null
Proceedings of SPIE - The International Society for Optical Engineering
Keywords
Field
DocType
non-empty universe,rough set,information system,maximal entropy,information entropy,partitions g,minimal entropy,average amount,relation v,graph-theoretical property,directed graph
Discrete mathematics,Graph,Combinatorics,Joint quantum entropy,Directed graph,Rough set,Partition (number theory),Entropy (information theory),Information measure,Mathematics,Maximum entropy probability distribution
Conference
Volume
Issue
ISSN
6104
null
null
ISBN
Citations 
PageRank 
3-540-28653-5
0
0.34
References 
Authors
3
3
Name
Order
Citations
PageRank
Cungen Cao130958.63
Yuefei Sui226641.52
Youming Xia361.89