通过采样对齐平均，提升神经数据循环坐标的鲁棒性
Subsampling, aligning, and averaging to find circular coordinates in recurrent time series
- 用拒绝采样校正采样密度不均，再通过普鲁克斯特匹配对齐平均
- 在蠕虫神经数据中发现可解释的脑状态环路与行为对应关系
- 适合处理不均匀采样、追求拓扑结构解释性的研究者使用
我们提出一种新算法，用于在预期存在重复模式的数据（如秀丽隐杆线虫神经记录）中寻找稳健的循环坐标。现有方法基于一维上同调类构建单纯复形上的循环坐标，但对采样密度不均极为敏感。本文提出新方法：先用拒绝采样纠正非均匀采样，再通过普鲁克斯特匹配对齐并平均子样本。该方法不仅显著提升坐标鲁棒性，还具有更好计算效率。我们在合成数据和真实神经活动记录上验证了该方法。结果揭示了线虫脑状态空间中由环路构成的拓扑模型，不同脑区状态可映射到特定可解释的宏观行为。
原文摘要 · Abstract (English)
We introduce a new algorithm for finding robust circular coordinates on data that is expected to exhibit recurrence, such as that which appears in neuronal recordings of C. elegans. Techniques exist to create circular coordinates on a simplicial complex from a dimension 1 cohomology class, and these can be applied to the Rips complex of a dataset when it has a prominent class in its dimension 1 cohomology. However, it is known this approach is extremely sensitive to uneven sampling density. Our algorithm comes with a new method to correct for uneven sampling density, adapting our prior work on averaging coordinates in manifold learning. We use rejection sampling to correct for inhomogeneous sampling and then apply Procrustes matching to align and average the subsamples. In addition to providing a more robust coordinate than other approaches, this subsampling and averaging approach has better efficiency. We validate our technique on both synthetic data sets and neuronal activity recordings. Our results reveal a topological model of neuronal trajectories for C. elegans that is constructed from loops in which different regions of the brain state space can be mapped to specific and interpretable macroscopic behaviors in the worm.
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