团拓扑揭示了神经相关性的内在几何结构
Clique topology reveals intrinsic geometric structure in neural correlations
摘要：
检测神经活动和连接数据中有意义的结构是具有挑战性的，在存在隐藏的非线性，其中传统的基于特征值的方法可能是误导。我们介绍了一种新的矩阵分析方法，称为团拓扑，提取非线性单调变换下的数据不变的功能。这些特征可用于检测随机结构和几何结构，并且仅依赖于矩阵元素的相对排序。然后，我们分析了大鼠海马锥体神经元的活动，记录，而动物正在探索一个二维的环境，并证实，我们的方法是能够检测几何组织只使用神经相关性的内在模式。值得注意的是，我们在非空间行为中发现了类似的结果，如车轮运行和REM睡眠。这表明，相关性的几何结构是由潜在的海马回路塑造的，而不仅仅是位置编码的结果。我们提出，团拓扑是一个强大的新工具，在生物环境中的矩阵分析，其中观察到的数量更有意义的变量的关系往往是非线性和未知的。
英文摘要：
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a two-dimensional environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during non-spatial behaviors such as wheel running and REM sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits, and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.
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