Algoritmi Center, University of Minho, 4800-058 Guimarães, Portugal.
CEiiA-Centro de Engenharia, Av. D. Afonso Henriques 1825, 4450-017 Matosinhos, Portugal.
Sensors (Basel). 2022 May 11;22(10):3657. doi: 10.3390/s22103657.
Persistent Homology (PH) analysis is a powerful tool for understanding many relevant topological features from a given dataset. PH allows finding clusters, noise, and relevant connections in the dataset. Therefore, it can provide a better view of the problem and a way of perceiving if a given dataset is equal to another, if a given sample is relevant, and how the samples occupy the feature space. However, PH involves reducing the problem to its simplicial complex space, which is computationally expensive and implementing PH in such Resource-Scarce Embedded Systems (RSES) is an essential add-on for them. However, due to its complexity, implementing PH in such tiny devices is considerably complicated due to the lack of memory and processing power. The following paper shows the implementation of 0-Dimensional Persistent Homology Analysis in a set of well-known RSES, using a technique that reduces the memory footprint and processing power needs of the 0-Dimensional PH algorithm. The results are positive and show that RSES can be equipped with this real-time data analysis tool.
持续同调（PH）分析是一种强大的工具，可用于从给定的数据集理解许多相关的拓扑特征。PH 允许在数据集中找到聚类、噪声和相关的连接。因此，它可以提供更好的问题视图，以及一种方法来判断给定的数据集是否等于另一个数据集，给定的样本是否相关，以及样本如何占据特征空间。然而，PH 涉及将问题简化到其单纯复形空间，这在计算上是昂贵的，并且在资源稀缺的嵌入式系统（RSES）中实现 PH 是它们的一个重要附加功能。然而，由于其复杂性，在如此小的设备中实现 PH 由于内存和处理能力的缺乏而变得相当复杂。本文展示了在一组著名的 RSES 中实现零维持续同调分析的方法，使用了一种可以降低零维 PH 算法的内存占用和处理能力需求的技术。结果是积极的，表明 RSES 可以配备这种实时数据分析工具。
