论文标题
使用拓扑自动编码器作为全球和本地拓扑的过滤功能
Using topological autoencoders as a filtering function for global and local topology
论文作者
论文摘要
由于其任意性和特定于域的要求，为映射器算法选择合适的过滤功能可能很困难。因此，找到可以在域上应用的一般过滤函数是令人感兴趣的，因为它将改善较高维度中的歧管的表示。在这个扩展的摘要中，我们提出拓扑自动编码器是适合此的候选者，并报告了最初的结果增强了一组高维流形的这一假设。结果表明，使用映射器算法时可以更轻松地选择过滤功能，从而可以对高维数据进行更通用和描述性表示。
Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest, since it would improve the representation of manifolds in higher dimensions. In this extended abstract, we propose that topological autoencoders is a suitable candidate for this and report initial results strengthening this hypothesis for one set of high-dimensional manifolds. The results indicate a potential for an easier choice of filtering function when using the Mapper algorithm, allowing for a more general and descriptive representation of high-dimensional data.
