{"title":"Parsimonious consensus hierarchies, partitions and fuzzy partitioning of a set of hierarchies","authors":"Ilaria Bombelli, Maurizio Vichi","doi":"10.1007/s11222-024-10415-7","DOIUrl":null,"url":null,"abstract":"<p>Methodology is described for fitting a fuzzy partition and a parsimonious consensus hierarchy (ultrametric matrix) to a set of hierarchies of the same set of objects. A model defining a fuzzy partition of a set of hierarchical classifications, with every class of the partition synthesized by a parsimonious consensus hierarchy is described. Each consensus includes an optimal consensus hard partition of objects and all the hierarchical agglomerative aggregations among the clusters of the consensus partition. The performances of the methodology are illustrated by an extended simulation study and applications to real data. A discussion is provided on the new methodology and some interesting future developments are described.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10415-7","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Methodology is described for fitting a fuzzy partition and a parsimonious consensus hierarchy (ultrametric matrix) to a set of hierarchies of the same set of objects. A model defining a fuzzy partition of a set of hierarchical classifications, with every class of the partition synthesized by a parsimonious consensus hierarchy is described. Each consensus includes an optimal consensus hard partition of objects and all the hierarchical agglomerative aggregations among the clusters of the consensus partition. The performances of the methodology are illustrated by an extended simulation study and applications to real data. A discussion is provided on the new methodology and some interesting future developments are described.
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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