Clustering and isolation in the consensus problem for partitions
type: Item
instance of: scholarly article
title: Clustering and isolation in the consensus problem for partitions
zbMATH Open document ID: 0624.62059
DOI: 10.1007/BF01894191
author: Dean A. Neumann
author: Victor T. jun. Norton
published in: Journal of Classification
publication date: 1986-01-01T00:00:00Z
review text: We examine the problem of aggregating several partitions of a finite set into a single consensus partition. We note that the dual concepts of clustering and isolation are especially significant in this connection. The hypothesis that a consensus partition should respect unanimity with respect to either concept leads us to stress a consensus interval rather than a single partition. The extremes of this inverval are characterized axiomatically. If a sufficient totality of traits has been measured, and if measurement errors are independent, then a ``true'' classifying partition can be expected to lie in the consensus interval. The structure of the partitions in the interval lends itself to partial solutions of the consensus problem. Conditional entropy may be used to quantify the uncertainty inherent in the interval as a whole.
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 4013784
zbMATH Keywords: lattice of partitions
zbMATH Keywords: consensus function
zbMATH Keywords: consensus partition
zbMATH Keywords: clustering
zbMATH Keywords: isolation
zbMATH Keywords: measurement errors
zbMATH Keywords: consensus interval
zbMATH Keywords: Conditional entropy
MaRDI profile type: Publication
cites work: Social choice and individual values
cites work: Multidimensional scaling of measures of distance between partitions
cites work: Metrics on spaces of finite trees
cites work: The complexity of computing metric distances between partitions
cites work: Q3887397
cites work: Efficient and binary consensus functions on transitively valued relations
cites work: Q5657424
full work available at URL: https://doi.org/10.1007/bf01894191
OpenAlex ID: W2088187868
Recommended article: Consensus of partitions: a constructive approach
Recommended article: A bound on partitioning clusters
Recommended article: On the parameterized complexity of consensus clustering
Recommended article: On the Parameterized Complexity of Consensus Clustering
Recommended article: A Biclustering Framework for Consensus Problems
Recommended article: An approach to cluster separability in a partition
Recommended article: Consensus-based partitions in the space of ordered partitions
Recommended article: Q5417662
description: scientific article; zbMATH DE number 4013784