Hard and Soft Euclidean Consensus Partitions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008

AUTHORS

Kurt Hornik , Walter Böhm

ABSTRACT

Euclidean partition dissimilarity d(P, P∼) (Dimitriadou et al., 2002) is defined as the square root of the minimal sum of squared differences of the class membership values of the partitions P and P∼, with the minimum taken over all matchings between the classes of the partitions. We first discuss some theoretical properties of this dissimilarity measure. Then, we look at the Euclidean consensus problem for partition ensembles, i.e., the problem to find a hard or soft partition P with a given number of classes which minimizes the (possibly weighted) sum Σbwbd(Pb,P)2 of squared Euclidean dissimilarities d between P and the elements Pb, of the ensemble. This is an NP-hard problem, and related to consensus problems studied in Gordon and Vichi (2001). We present an efficient “Alternating Optimization” (AO) heuristic for finding P, which iterates between optimally rematching classes for fixed memberships, and optimizing class memberships for fixed matchings. An implementation of such AO algorithms for consensus partitions is available in the R extension package clue. We illustrate this algorithm on two data sets (the popular Rosenberg-Kim kinship terms data and a macroeconomic one) employed by Gordon & Vichi. More... »

PAGES

147-154

Book

TITLE

Data Analysis, Machine Learning and Applications

ISBN

978-3-540-78239-1
978-3-540-78246-9

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-78246-9_18

DOI

http://dx.doi.org/10.1007/978-3-540-78246-9_18

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1012201657


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