传染动力学的流形学习

感染性传染地图利用激活次阈值分配向量在高维欧氏空间节点的网络。作为传染病地图图像的点云既反映了网络的底层结构，也反映了传染病在网络上的传播行为。直观地说，如果传染病沿着该结构传播，那么这样的点云展示了网络底层结构的特征，这一观察表明，传染图是一种可行的多形学习技术。我们在许多不同的真实世界和合成数据集上测试传染映射作为一种流形学习工具，并将其性能与最著名的流形学习算法之一Isomap进行比较。我们发现，在一定条件下，在有噪声的数据中，传染病映射能够可靠地检测底层流形结构，而Isomap由于噪声引起的误差而失效。这巩固了传染病映射作为一种多方面学习的技术。

原文：Contagion maps exploit activation times in threshold contagions to assign vectors in high-dimensional Euclidean space to the nodes of a network. A point cloud that is the image of a contagion map reflects both the structure underlying the network and the spreading behaviour of the contagion on it. Intuitively, such a point cloud exhibits features of the network's underlying structure if the contagion spreads along that structure, an observation which suggests contagion maps as a viable manifold-learning technique. We test contagion maps as a manifold-learning tool on a number of different real-world and synthetic data sets, and we compare their performance to that of Isomap, one of the most well-known manifold-learning algorithms. We find that, under certain conditions, contagion maps are able to reliably detect underlying manifold structure in noisy data, while Isomap fails due to noise-induced error. This consolidates contagion maps as a technique for manifold learning.