Topological data analysis, such as persistent homology has shown beneficial properties for machine learning in many tasks. Topological representations, such as the persistence diagram (PD), however, have a complex structure (multiset of intervals) which makes it difficult to combine with typical machine learning workflows. We present novel compact fixed-size vectorial representations of PDs based on clustering and bag of words encodings that cope well with the inherent sparsity of PDs. Our novel representations outperform state-of-the-art approaches from topological data analysis and are computationally more efficient.

中文翻译：

---

用于拓扑数据分析的持久性码本

拓扑数据分析，例如持久同源性，已在许多任务中显示出对机器学习有益的特性。然而，诸如持久性图 (PD) 之类的拓扑表示具有复杂的结构（多组区间），这使得它难以与典型的机器学习工作流程相结合。我们提出了基于聚类和词袋编码的 PD 的新颖紧凑的固定大小向量表示，可以很好地应对 PD 的固有稀疏性。我们的新颖表示优于拓扑数据分析的最新方法，并且在计算上更有效。