光谱连通性分析

摘要：

谱核方法是用于将数据转换到坐标系中的技术，该坐标系有效地揭示了数据的几何结构，特别是“连通性”。这些方法依赖于某些调整参数。我们分析了这些调谐参数的方法的依赖性。我们专注于一种特定的技术-扩散映射-但我们的分析也可以用于其他方法。我们确定人口数量隐含估计，我们解释了这些方法与经典的核平滑，我们定义了一个适当的风险函数分析估计。我们还表明，在某些情况下，快速收敛速度是可能的，即使在高维。

英文摘要：

Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We analyze the dependence of the method on these tuning parameters. We focus on one particular technique - diffusion maps - but our analysis can be used for other methods as well. We identify the population quantities implicitly being estimated, we explain how these methods relate to classical kernel smoothing and we define an appropriate risk function for analyzing the estimators. We also show that, in some cases, fast rates of convergence are possible even in high dimensions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。