论文标题
感知：使用拓扑数据分析的一种新的在线更改点检测方法
PERCEPT: a new online change-point detection method using topological data analysis
论文作者
论文摘要
拓扑数据分析（TDA）提供了一组数据分析工具，用于从复杂的高维数据集中提取嵌入式拓扑结构。近年来，TDA是一个快速增长的领域，在广泛的应用中发现了成功，包括信号处理，神经科学和网络分析。在这些应用程序中，在线检测变化至关重要，但是这可能是极具挑战性的，因为这种变化通常发生在高维数据流中的低维嵌入中。因此，我们提出了一种新方法，称为基于持久图的更改点检测（感知），该方法利用了从TDA到依次检测变化的学习拓扑结构。感知遵循两个关键步骤：它首先通过持久图将嵌入式拓扑作为点云学习，然后应用一种非参数监视方法来检测所得点云分布的变化。这产生了一个非参数，拓扑感知的框架，可以有效地检测出高维数据流的在线变化。我们研究了在数据流具有嵌入式拓扑结构的数值实验套件中，感知对现有方法的有效性。然后，我们证明了在太阳耀斑监测和人类手势检测中，感知在两个应用中的有用性。
Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in a low-dimensional embedding within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a non-parametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a non-parametric, topology-aware framework which can efficiently detect online changes from high-dimensional data streams. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications in solar flare monitoring and human gesture detection.
