Detecting local perturbations of networks in a latent hyperbolic embedding space
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914828788957184 |
|---|---|
| author | Longhena, Alice Guillemaud, Martin Chavez, Mario |
| author_facet | Longhena, Alice Guillemaud, Martin Chavez, Mario |
| contents | Graph theoretical approaches have been proven to be effective in the characterization of connected systems, as well as in quantifying their dysfunction due to perturbation. In this paper, we show the advantage of a non-Euclidean (hyperbolic) representation of networks to identify local connectivity perturbations and to characterize the induced effects on a large scale. We propose two perturbation scores based on representations of the networks in a latent geometric space, obtained through an embedding onto the hyperbolic Poincaré disk. We numerically demonstrate that these methods are able to localize perturbations in networks with homogeneous or heterogeneous degree connectivity. We apply this framework to identify the most perturbed brain areas in epileptic patients following surgery. This study is conceived in the effort of developing more powerful tools to represent and analyze brain networks, and it is the first to apply geometric network embedding techniques to the case of epilepsy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting local perturbations of networks in a latent hyperbolic embedding space Longhena, Alice Guillemaud, Martin Chavez, Mario Quantitative Methods Data Analysis, Statistics and Probability Graph theoretical approaches have been proven to be effective in the characterization of connected systems, as well as in quantifying their dysfunction due to perturbation. In this paper, we show the advantage of a non-Euclidean (hyperbolic) representation of networks to identify local connectivity perturbations and to characterize the induced effects on a large scale. We propose two perturbation scores based on representations of the networks in a latent geometric space, obtained through an embedding onto the hyperbolic Poincaré disk. We numerically demonstrate that these methods are able to localize perturbations in networks with homogeneous or heterogeneous degree connectivity. We apply this framework to identify the most perturbed brain areas in epileptic patients following surgery. This study is conceived in the effort of developing more powerful tools to represent and analyze brain networks, and it is the first to apply geometric network embedding techniques to the case of epilepsy. |
| title | Detecting local perturbations of networks in a latent hyperbolic embedding space |
| topic | Quantitative Methods Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2401.13495 |