Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
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DOI：
10.1137/20m1324089
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发表时间：
2021-01-01
影响因子：
3.6
通讯作者：
Wu, Kaiyi
中科院分区：
文献类型：
--
作者：
Cowen, Lenore;Devkota, Kapil;Wu, Kaiyi
数据相关度量是学习高维数据底层结构的强大工具。本文进一步开发和分析了一种称为扩散状态距离（DSD）的数据相关度量，该度量使用数据驱动的扩散过程来比较点。与相关的扩散方法不同，数据集定义包含跨时间尺度的信息，这允许以无参数的方式推断内在数据结构。本文发展了一个理论的基础上出现的介观平衡在底层的扩散过程中的DSD。本文还提出了基于DSD的去噪和降维新算法，并进行了分析。这些方法是基于一个加权谱分解的基础扩散过程，和合成数据集和真实的生物网络的实验说明了所提出的算法的效率在速度和准确性。在整个过程中，与相关的方法进行比较，以说明DSD的显着优势，表现出多尺度结构的数据集。
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article further develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a data-driven diffusion process. Unlike related diffusion methods, DSDs incorporate information across time scales, which allows for the intrinsic data structure to be inferred in a parameter-free manner. This article develops a theory for DSD based on the multitemporal emergence of mesoscopic equilibria in the underlying diffusion process. New algorithms for denoising and dimension reduction with DSD are also proposed and analyzed. These approaches are based on a weighted spectral decomposition of the underlying diffusion process, and experiments on synthetic datasets and real biological networks illustrate the efficacy of the proposed algorithms in terms of both speed and accuracy. Throughout, comparisons with related methods are made in order to illustrate the distinct advantages of DSD for datasets exhibiting multiscale structure.