Abstract Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant. In addition, we describe two new stable summary functions combining persistent entropy and the Betti curve. Finally, we use the previously defined summary functions in a material classification task to show their usefulness in machine learning and pattern recognition.

中文翻译：

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关于拓扑数据分析的持久熵和新汇总函数的稳定性

摘要 持久同源性和持久熵最近已成为模式识别的有用工具。在本文中，我们找到了持久熵对输入数据中的小扰动保持稳定和尺度不变的要求。此外，我们描述了结合持久熵和 Betti 曲线的两个新的稳定汇总函数。最后，我们在材料分类任务中使用先前定义的汇总函数来展示它们在机器学习和模式识别中的有用性。