论文标题
通过交织优化降低拓扑的维度
Topology-Preserving Dimensionality Reduction via Interleaving Optimization
论文作者
论文摘要
降低降低技术是用于数据预处理和可视化的强大工具，通常很少有关于嵌入拓扑正确性的保证。可以使用越野透过过滤的持续同源性之间的相互交织距离来识别一个量表，在该规模的拓扑特征，例如嵌入式和原始数据集中的簇或孔中的孔。我们展示了如何将寻求最小化交织距离的优化融合到维度降低算法中，并明确证明其在寻找最佳线性投影时的使用。我们证明了该框架对数据可视化的实用性。
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the persistent homology of Vietoris-Rips filtrations can be used to identify a scale at which topological features such as clusters or holes in an embedding and original data set are in correspondence. We show how optimization seeking to minimize the interleaving distance can be incorporated into dimensionality reduction algorithms, and explicitly demonstrate its use in finding an optimal linear projection. We demonstrate the utility of this framework to data visualization.
