| Full text | |
| Author(s): |
Doraiswamy, Harish
[1]
;
Tierny, Julien
[2, 3]
;
Silva, Paulo J. S.
[4]
;
Nonato, Luis Gustavo
[5]
;
Silva, Claudio
[1]
Total Authors: 5
|
| Affiliation: | [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
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS; v. 27, n. 2, p. 561-571, FEB 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 18/07551-6 - Optimization Methods for Data Analysis and Machine Learning |
| Grantee: | Paulo José da Silva e Silva |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 16/04190-7 - Visualizing and Analyzing Urban Data: Mathematical and Computational Aspects |
| Grantee: | Luis Gustavo Nonato |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |