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We typically assume that we have a discrete data set \(X=\{x_1,x_2,\dots ,x_N\}\) , equipped with some distance function \(d_X(.,.)\) between the data points. Often such data are sampled from some ambient space, which is Euclidean space in many applications., i.e. \(x_i\in \mathbb {R}^n\) . We furthermore assume that the data shows certain dependencies and regularities and therefore has fewer intrinsic degrees of freedom than the number n of dimensions or the number N of samples, and finally, that it is amenable to continuous interpolation, i.e. that there is a way to infer the possible positions of data points that have not yet been sampled.

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Introduction

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Lukas Silvester Barth,
  • Hannaneh Fahimi,
  • Parvaneh Joharinad,
  • Jürgen Jost,
  • Janis Keck

摘要

We typically assume that we have a discrete data set \(X=\{x_1,x_2,\dots ,x_N\}\) , equipped with some distance function \(d_X(.,.)\) between the data points. Often such data are sampled from some ambient space, which is Euclidean space in many applications., i.e. \(x_i\in \mathbb {R}^n\) . We furthermore assume that the data shows certain dependencies and regularities and therefore has fewer intrinsic degrees of freedom than the number n of dimensions or the number N of samples, and finally, that it is amenable to continuous interpolation, i.e. that there is a way to infer the possible positions of data points that have not yet been sampled.