一种快速的$\mathcal{L}_p$峰电位对齐度量
A Fast $\mathcal{L}_p$ Spike Alignment Metric
摘要：
神经反应空间的度量化是一个正在进行的研究计划，旨在寻找自然的方法来描述，在几何术语，在大脑中的可能活动的集合。该程序的一个组成部分是{ \em尖峰度量}，即从神经元记录的两个脉冲序列之间的距离的概念。对准尖峰度量通过识别一个训练和另一个中的“等效”尖峰来工作。我们提出了一个对齐尖峰度量具有$\mathcal{L}_p$底层几何结构; $\mathcal{L}_2$版本是欧几里德的，并且适合于通过多维标度方法或相关程序进一步嵌入欧几里德空间。我们将展示如何实现一个快速算法的计算这个度量的基础上二分图匹配理论。
英文摘要：
The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the {\em spike metrics}, notions of distance between two spike trains recorded from a neuron. Alignment spike metrics work by identifying "equivalent" spikes in one train and the other. We present an alignment spike metric having $\mathcal{L}_p$ underlying geometrical structure; the $\mathcal{L}_2$ version is Euclidean and is suitable for further embedding in Euclidean spaces by Multidimensional Scaling methods or related procedures. We show how to implement a fast algorithm for the computation of this metric based on bipartite graph matching theory.
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