We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density of the zeros of the Lagrange function, showing that they scale with the density of the data. These results indicate that Lagrange-type bases are ideal building blocks for analyzing data on graphs, and we illustrate their use in kernel-based machine learning applications.

中文翻译：

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在图上插补样条曲线以用于数据科学应用

我们为基于图的数据引入内插基础，并推导这些基础的属性。证明了多谐Lagrange函数可以满足远离其中心的指数衰减。衰减取决于拉格朗日函数的零点的密度，表明它们随数据的密度成比例。这些结果表明，拉格朗日类型的基础是用于分析图上数据的理想构建基块，并且我们说明了它们在基于内核的机器学习应用程序中的使用。