Advances in self-organizing maps for their application to compositional data
A self-organizing map (SOM) is a non-linear projection of a D-dimensional data set, where the distance among observations is approximately preserved on to a lower dimensional space. The SOM arranges multivariate data based on their similarity to each other by allowing pattern recognition leading to...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10256/24188 |
| Acesso em linha: | http://hdl.handle.net/10256/24188 |
| Access Level: | acceso abierto |
| Palavra-chave: | Aitchison, Geometria d' Aitchison Geometry Anàlisi composicional Compositional analysis Projecció isomètrica Isometric projection Ràtio i proporció Ratio and proportion Aprenentatge automàtic Machine learning Estadística matemàtica -- Informàtica Mathematical statistics -- Data processing |
| Resumo: | A self-organizing map (SOM) is a non-linear projection of a D-dimensional data set, where the distance among observations is approximately preserved on to a lower dimensional space. The SOM arranges multivariate data based on their similarity to each other by allowing pattern recognition leading to easier interpretation of higher dimensional data. The SOM algorithm allows for selection of different map topologies, distances and parameters, which determine how the data will be organized on the map. In the particular case of compositional data (such as elemental, mineralogical, or maceral abundance), the sample space is governed by Aitchison geometry and extra steps are required prior to their SOM analysis. Following the principle of working on log-ratio coordinates, the simplicial operations and the Aitchison distance, which are appropriate elements for the SOM, are presented. With this structure developed, a SOM using Aitchison geometry is applied to properly interpret elemental data from combustion products (bottom ash, fly ash, and economizer fly ash) in a Wyoming coal-fired power plant. Results from this effort provide knowledge about the differences between the ash composition in the coal combustion process |
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