持续同源性的统计推断应用于模拟fMRI时间序列数据

IF 1.7 Q2 MATHEMATICS, APPLIED
H. Abdallah, Adam J. Regalski, Mohammad Behzad Kang, Maria Berishaj, N. Nnadi, Asadur Chowdury, V. Diwadkar, A. Salch
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引用次数: 3

摘要

时间序列数据是生物医学科学中最广泛使用的数据之一,包括功能磁共振成像(fMRI)等领域。拓扑数据分析(TDA)工具可以捕获时间序列数据中的结构。持久化同构是TDA中最常用的数据分析工具,它可以有效地将复杂的高维数据总结为可解释的二维表示,称为持久化图。现有的数据持久同调的统计推断方法依赖于一个独立性假设的满足。虽然时间序列中的每个时间指标都可以计算出持久的同源性,但时间序列数据往往不能满足独立性假设。本文提出了一种统计检验方法,通过使用一组持久性图实现多级块采样蒙特卡罗检验,消除了独立性假设。然后在模拟的fMRI数据上证明了其检测任务相关拓扑组织的有效性。因此,这种新的统计检验适用于分析fMRI数据的持续同源性,以及一般的非独立数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical inference for persistent homology applied to simulated fMRI time series data
Time-series data are amongst the most widely-used in biomedical sciences, including domains such as functional Magnetic Resonance Imaging (fMRI). Structure within time series data can be captured by the tools of topological data analysis (TDA). Persistent homology is the mostly commonly used data-analytic tool in TDA, and can effectively summarize complex high-dimensional data into an interpretable 2-dimensional representation called a persistence diagram. Existing methods for statistical inference for persistent homology of data depend on an independence assumption being satisfied. While persistent homology can be computed for each time index in a time-series, time-series data often fail to satisfy the independence assumption. This paper develops a statistical test that obviates the independence assumption by implementing a multi-level block sampled Monte Carlo test with sets of persistence diagrams. Its efficacy for detecting task-dependent topological organization is then demonstrated on simulated fMRI data. This new statistical test is therefore suitable for analyzing persistent homology of fMRI data, and of non-independent data in general.
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CiteScore
3.30
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