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Daunis i Estadella, Josep
MartÃn Fernández, Josep Antoni |
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Universitat de Girona. Departament d’Informà tica i Matemà tica Aplicada | |
Cortés, JoaquÃn A.
Palma, José Luis |
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Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data Geologische Vereinigung; Institut d’EstadÃstica de Catalunya; International Association for Mathematical Geology; Cà tedra LluÃs Santaló d’Aplicacions de la Matemà tica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010. |
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http://hdl.handle.net/2072/14758 | |
eng | |
Universitat de Girona. Departament d’Informà tica i Matemà tica Aplicada | |
Tots els drets reservats | |
Meteorologia -- Models estadÃstics
Anà lisi multivariable |
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Using self organizing maps on compositional data | |
info:eu-repo/semantics/conferenceObject | |
Recercat |