论文标题
神经元形态的拓扑描述符的稳定性
Stability of topological descriptors for neuronal morphology
论文作者
论文摘要
神经元的拓扑形态描述符是与表示为树的神经元形状相关的间隔的多组。在实践中，拓扑形态描述符使用持久图像进行矢量形式，这可以帮助对广泛神经元组的形态进行分类和表征。我们研究了对神经元形态的小变化，拓扑形态描述源的稳定性。我们表明，神经元的拓扑形态描述产生的持久图对于1-wasserstein距离与对树的一系列扰动是稳定的。这些结果确保了拓扑形态描述符的持久性图像在相同的扰动和可靠的相同集合中稳定。
The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can help classify and characterize the morphology of broad groups of neurons. We study the stability of topological morphology descriptors under small changes to neuronal morphology. We show that the persistence diagram arising from the topological morphology descriptor of a neuron is stable for the 1-Wasserstein distance against a range of perturbations to the tree. These results guarantee that persistence images of topological morphology descriptors are stable against the same set of perturbations and reliable.
