期刊
JOURNAL OF MACHINE LEARNING RESEARCH
卷 18, 期 -, 页码 -出版社
MICROTOME PUBL
关键词
topological data analysis; persistence diagrams; kernel method; kernel embedding; persistence weighted Gaussian kernel
资金
- JST CREST Mathematics [15656429]
- JSPS KAKENHI [26540016]
- Structural Materials for Innovation Strategic Innovation Promotion Program [D72]
- Information Integration Initiative (MI2I) project of the Support Program for Starting Up, Innovation Hub from JST
- JSPS [17J02401]
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complicated data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, distinguishing robust and noisy topological properties. This paper introduces a kernel method for persistence diagrams to develop a statistical framework in TDA. The proposed kernel is stable under perturbation of data, enables one to explicitly control the effect of persistence by a weight function, and allows an efficient and accurate approximate computation. The method is applied into practical data on granular systems, oxide glasses and proteins, showing advantages of our method compared to other relevant methods for persistence diagrams.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据