Dimensional reduction of gradient-like stochastic systems with multiplicative noise via Fokker-Planck diffusion maps
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_ | 1866929200811737088 |
|---|---|
| author | Baumgartner, Andrew Huang, Sui Hadlock, Jennifer Funk, Cory |
| author_facet | Baumgartner, Andrew Huang, Sui Hadlock, Jennifer Funk, Cory |
| contents | Dimensional reduction techniques have long been used to visualize the structure and geometry of high dimensional data. However, most widely used techniques are difficult to interpret due to nonlinearities and opaque optimization processes. Here we present a specific graph based construction for dimensionally reducing continuous stochastic systems with multiplicative noise moving under the influence of a potential. To achieve this, we present a specific graph construction which generates the Fokker-Planck equation of the stochastic system in the continuum limit. The eigenvectors and eigenvalues of the normalized graph Laplacian are used as a basis for the dimensional reduction and yield a low dimensional representation of the dynamics which can be used for downstream analysis such as spectral clustering. We focus on the use case of single cell RNA sequencing data and show how current diffusion map implementations popular in the single cell literature fit into this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimensional reduction of gradient-like stochastic systems with multiplicative noise via Fokker-Planck diffusion maps Baumgartner, Andrew Huang, Sui Hadlock, Jennifer Funk, Cory Quantitative Methods Biological Physics Cell Behavior Genomics Dimensional reduction techniques have long been used to visualize the structure and geometry of high dimensional data. However, most widely used techniques are difficult to interpret due to nonlinearities and opaque optimization processes. Here we present a specific graph based construction for dimensionally reducing continuous stochastic systems with multiplicative noise moving under the influence of a potential. To achieve this, we present a specific graph construction which generates the Fokker-Planck equation of the stochastic system in the continuum limit. The eigenvectors and eigenvalues of the normalized graph Laplacian are used as a basis for the dimensional reduction and yield a low dimensional representation of the dynamics which can be used for downstream analysis such as spectral clustering. We focus on the use case of single cell RNA sequencing data and show how current diffusion map implementations popular in the single cell literature fit into this framework. |
| title | Dimensional reduction of gradient-like stochastic systems with multiplicative noise via Fokker-Planck diffusion maps |
| topic | Quantitative Methods Biological Physics Cell Behavior Genomics |
| url | https://arxiv.org/abs/2401.03095 |