Visualizing Shape Functionals via Sinkhorn Multidimensional Scaling
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909322266542080 |
|---|---|
| author | Yachimura, Toshiaki Okamoto, Jun Cavallina, Lorenzo |
| author_facet | Yachimura, Toshiaki Okamoto, Jun Cavallina, Lorenzo |
| contents | In this paper, we present Sinkhorn multidimensional scaling (Sinkhorn MDS) as a method for visualizing shape functionals in shape spaces. This approach uses the Sinkhorn divergence to map these infinite-dimensional spaces into lower-dimensional Euclidean spaces. We establish error estimates for the embedding generated by Sinkhorn MDS compared to the unregularized case. Moreover, we validate the method through numerical experiments, including visualizations of the classical Dido's problem and two newly introduced shape functionals: the double-well and Sinkhorn cone-type shape functionals. Our results demonstrate that Sinkhorn MDS effectively captures and visualizes shapes of shape functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Visualizing Shape Functionals via Sinkhorn Multidimensional Scaling Yachimura, Toshiaki Okamoto, Jun Cavallina, Lorenzo Optimization and Control Metric Geometry 49Q10, 49Q22, 62H20, 68T10 In this paper, we present Sinkhorn multidimensional scaling (Sinkhorn MDS) as a method for visualizing shape functionals in shape spaces. This approach uses the Sinkhorn divergence to map these infinite-dimensional spaces into lower-dimensional Euclidean spaces. We establish error estimates for the embedding generated by Sinkhorn MDS compared to the unregularized case. Moreover, we validate the method through numerical experiments, including visualizations of the classical Dido's problem and two newly introduced shape functionals: the double-well and Sinkhorn cone-type shape functionals. Our results demonstrate that Sinkhorn MDS effectively captures and visualizes shapes of shape functionals. |
| title | Visualizing Shape Functionals via Sinkhorn Multidimensional Scaling |
| topic | Optimization and Control Metric Geometry 49Q10, 49Q22, 62H20, 68T10 |
| url | https://arxiv.org/abs/2409.14687 |