Non-Euclidean Self-Organizing Maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
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| _version_ | 1866909282750955520 |
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| author | Celińska-Kopczyńska, Dorota Kopczyński, Eryk |
| author_facet | Celińska-Kopczyńska, Dorota Kopczyński, Eryk |
| contents | Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11769 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-Euclidean Self-Organizing Maps Celińska-Kopczyńska, Dorota Kopczyński, Eryk Machine Learning Neural and Evolutionary Computing Geometric Topology Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical). |
| title | Non-Euclidean Self-Organizing Maps |
| topic | Machine Learning Neural and Evolutionary Computing Geometric Topology |
| url | https://arxiv.org/abs/2109.11769 |