Topological Machine Learning with Persistence Indicator Functions
Topological Machine Learning with Persistence Indicator Functions
复制标题
具有持久性指示函数的拓扑机器学习
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
H. Leitte
中科院分区：
文献类型：
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作者：
Bastian Alexander Rieck;F. Sadlo;H. Leitte
来自计算拓扑学的技术，特别是持久同调，正变得越来越与数据分析相关。其稳定的指标允许使用许多基于距离的数据分析方法，例如多维缩放，同时提供了坚实的理论基础。然而，许多现代机器学习算法都是基于核的。本文提出了持续性指示器函数(PIF)，它总结了持续性图，即拓扑数据分析中的特征描述符。PIF可以在线性时间内计算和比较，并且具有许多有益的性质，例如基于核的相似性度量的可用性。我们演示了它们在常见数据分析场景中的用法，例如复杂结构化数据的置信度估计和分类。
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based on kernels. This paper presents persistence indicator functions (PIFs), which summarize persistence diagrams, i.e., feature descriptors in topological data analysis. PIFs can be calculated and compared in linear time and have many beneficial properties, such as the availability of a kernel-based similarity measure. We demonstrate their usage in common data analysis scenarios, such as confidence set estimation and classification of complex structured data.
DOI：
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发表时间：
2015-07
期刊：
J. Mach. Learn. Res.
影响因子：
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作者：
Henry Adams;T. Emerson;M. Kirby;R. Neville;C. Peterson;Patrick D. Shipman;Sofya Chepushtanova;Eric M. Hanson;Francis C. Motta;Lori Ziegelmeier
通讯作者：
Henry Adams;T. Emerson;M. Kirby;R. Neville;C. Peterson;Patrick D. Shipman;Sofya Chepushtanova;Eric M. Hanson;Francis C. Motta;Lori Ziegelmeier