论文标题
Lebesgue点的最近邻居表征在度量度量空间中
A Nearest Neighbor Characterization of Lebesgue Points in Metric Measure Spaces
论文作者
论文摘要
事实证明，几乎每个观点的属性都是Lebesgue点，对于基于最近的邻居的几种分类算法的一致性至关重要。我们以1个最新的邻居回归算法的估计来表征Lebesgue点，从而在相应的收敛问题中脱颖而出，脱颖而出。然后，我们给出了结果的应用，证明了在一般度量空间中大量一类最邻居分类算法的风险的融合，几乎每个点都是lebesgue点。
The property of almost every point being a Lebesgue point has proven to be crucial for the consistency of several classification algorithms based on nearest neighbors. We characterize Lebesgue points in terms of a 1-Nearest Neighbor regression algorithm for pointwise estimation, fleshing out the role played by tie-breaking rules in the corresponding convergence problem. We then give an application of our results, proving the convergence of the risk of a large class of 1-Nearest Neighbor classification algorithms in general metric spaces where almost every point is a Lebesgue point.
