Hdl Handle:
http://hdl.handle.net/10545/621146
Title:
Direct reading algorithm for hierarchical clustering
Authors:
Murtagh, Fionn ( 0000-0002-0589-6892 ) ; Contreras, Pedro
Abstract:
Reading the clusters from a data set such that the overall computational complexity is linear in both data dimensionality and in the number of data elements has been carried out through filtering the data in wavelet transform space. This objective is also carried out after an initial transforming of the data to a canonical order. Including high dimensional, high cardinality data, such a canonical order is provided by row and column permutations of the data matrix. In our recent work, we induce a hierarchical clustering from seriation through unidimensional representation of our observations. This linear time hierarchical classification is directly derived from the use of the Baire metric, which is simultaneously an ultrametric. In our previous work, the linear time construction of a hierarchical clustering is studied from the following viewpoint: representing the hierarchy initially in an m-adic, m =10, tree representation, followed by decreasing m to smaller valued representations that include p-adic representations, where p is prime and m is a non-prime positive integer. This has the advantage of facilitating a more direct visualization and hence interpretation of the hierarchy. In this work we present further case studies and examples of how this approach is very advantageous for such an ultrametric topological data mapping.
Affiliation:
University of Derby; Thinking Safe Ltd.
Citation:
Murtagh, F. and Contreras, P. (2016) 'Direct Reading Algorithm for Hierarchical Clustering', Electronic Notes in Discrete Mathematics, 56:37
Publisher:
Elsevier
Journal:
Electronic Notes in Discrete Mathematics
Issue Date:
1-Dec-2016
URI:
http://hdl.handle.net/10545/621146
DOI:
10.1016/j.endm.2016.11.006
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S157106531630213X
Type:
Article
Language:
en
ISSN:
15710653
Appears in Collections:
Department of Electronics, Computing & Maths

Full metadata record

DC FieldValue Language
dc.contributor.authorMurtagh, Fionnen
dc.contributor.authorContreras, Pedroen
dc.date.accessioned2016-12-12T09:30:56Z-
dc.date.available2016-12-12T09:30:56Z-
dc.date.issued2016-12-01-
dc.identifier.citationMurtagh, F. and Contreras, P. (2016) 'Direct Reading Algorithm for Hierarchical Clustering', Electronic Notes in Discrete Mathematics, 56:37en
dc.identifier.issn15710653-
dc.identifier.doi10.1016/j.endm.2016.11.006-
dc.identifier.urihttp://hdl.handle.net/10545/621146-
dc.description.abstractReading the clusters from a data set such that the overall computational complexity is linear in both data dimensionality and in the number of data elements has been carried out through filtering the data in wavelet transform space. This objective is also carried out after an initial transforming of the data to a canonical order. Including high dimensional, high cardinality data, such a canonical order is provided by row and column permutations of the data matrix. In our recent work, we induce a hierarchical clustering from seriation through unidimensional representation of our observations. This linear time hierarchical classification is directly derived from the use of the Baire metric, which is simultaneously an ultrametric. In our previous work, the linear time construction of a hierarchical clustering is studied from the following viewpoint: representing the hierarchy initially in an m-adic, m =10, tree representation, followed by decreasing m to smaller valued representations that include p-adic representations, where p is prime and m is a non-prime positive integer. This has the advantage of facilitating a more direct visualization and hence interpretation of the hierarchy. In this work we present further case studies and examples of how this approach is very advantageous for such an ultrametric topological data mapping.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S157106531630213Xen
dc.rightsArchived with thanks to Electronic Notes in Discrete Mathematicsen
dc.subjectAnalyticsen
dc.subjectHierarchical clusteringen
dc.subjectUltrametric topologyen
dc.subjectNumber representationen
dc.subjectLinear time computational complexityen
dc.titleDirect reading algorithm for hierarchical clusteringen
dc.typeArticleen
dc.contributor.departmentUniversity of Derbyen
dc.contributor.departmentThinking Safe Ltd.en
dc.identifier.journalElectronic Notes in Discrete Mathematicsen
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