| Texto completo | |
| Autor(es): |
Doraiswamy, Harish
[1]
;
Tierny, Julien
[2, 3]
;
Silva, Paulo J. S.
[4]
;
Nonato, Luis Gustavo
[5]
;
Silva, Claudio
[1]
Número total de Autores: 5
|
| Afiliação do(s) autor(es): | [1] NYU, New York, NY 10003 - USA
[2] CNRS, Paris - France
[3] Sorbonne Univ, Paris - France
[4] Univ Estadual Campinas, Campinas - Brazil
[5] Univ Sao Paulo, Sao Carlos - Brazil
Número total de Afiliações: 5
|
| Tipo de documento: | Artigo Científico |
| Fonte: | IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS; v. 27, n. 2, p. 561-571, FEB 2021. |
| Citações Web of Science: | 0 |
| Resumo | |
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example. In fact, although adopting distinct mathematical formulations designed to favor different aspects of the data, most multidimensional projection methods strive to preserve dissimilarity measures that encapsulate geometric properties such as distances or the proximity relation between data objects. However, geometric relations are not the only interesting property to be preserved in a projection. For instance, the analysis of particular structures such as clusters and outliers could be more reliably performed if the mapping process gives some guarantee as to topological invariants such as connected components and loops. This paper introduces TopoMap, a novel projection technique which provides topological guarantees during the mapping process. In particular, the proposed method performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods. (AU) | |
| Processo FAPESP: | 18/07551-6 - Métodos de Otimização para Análise de Dados e Aprendizagem de Máquina |
| Beneficiário: | Paulo José da Silva e Silva |
| Modalidade de apoio: | Bolsas no Exterior - Pesquisa |
| Processo FAPESP: | 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria |
| Beneficiário: | Francisco Louzada Neto |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |
| Processo FAPESP: | 16/04190-7 - Análise e Visualização de Dados Urbanos: aspectos matemáticos e computacionais |
| Beneficiário: | Luis Gustavo Nonato |
| Modalidade de apoio: | Bolsas no Exterior - Pesquisa |
| Processo FAPESP: | 18/24293-0 - Métodos computacionais de otimização |
| Beneficiário: | Sandra Augusta Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |