Mahler Barbara I
Mathematical Institute, University of Oxford, Oxford, United Kingdom.
Front Big Data. 2022 Apr 26;5:668356. doi: 10.3389/fdata.2022.668356. eCollection 2022.
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 behavior 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 and variants thereof as a manifold-learning tool on a number of different synthetic and real-world 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. We also demonstrate that processing distance estimates between data points before performing methods to determine geometry, topology and dimensionality of a data set leads to clearer results for both Isomap and contagion maps.
传播映射利用阈值传播中的激活时间，将高维欧几里得空间中的向量分配给网络的节点。作为传播映射图像的点云既反映了网络的底层结构，也反映了传播在该网络上的传播行为。直观地说，如果传播沿着该结构进行，这样的点云就会展现出网络底层结构的特征，这一观察结果表明传播映射是一种可行的流形学习技术。我们在多个不同的合成数据集和真实世界数据集上，将传播映射及其变体作为一种流形学习工具进行测试，并将它们的性能与最著名的流形学习算法之一等距映射（Isomap）的性能进行比较。我们发现，在某些条件下，传播映射能够可靠地检测噪声数据中的底层流形结构，而等距映射则因噪声引起的误差而失败。这巩固了传播映射作为一种流形学习技术的地位。我们还证明，在执行确定数据集的几何、拓扑和维度的方法之前，对数据点之间的距离估计进行处理，会使等距映射和传播映射都得到更清晰的结果。
