Dimensional reduction of gradient-like stochastic systems with multiplicative noise via Fokker-Planck diffusion maps
arxiv(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要