Corbet René, Fugacci Ulderico, Kerber Michael, Landi Claudia, Wang Bei
Graz University of Technology, Austria.
University of Modena and Reggio Emilia, Italy.
Comput Graph X. 2019 Dec;2. doi: 10.1016/j.cagx.2019.100005. Epub 2019 Jun 6.
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques with applicability on shape analysis, recognition and classification. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.
拓扑数据分析及其主要方法——持久同调，为计算高维且有噪声数据集的拓扑信息提供了一个工具包。单参数持久同调的核已被建立起来，以便将持久同调与适用于形状分析、识别和分类的机器学习技术联系起来。我们通过整合沿直线加权的单参数核来构建多参数持久性的核。我们证明了我们的核是稳定且可有效计算的，这在拓扑数据分析和用于多变量数据分析的机器学习之间建立了理论联系。
