Kernel-based techniques have become a common way for describing the local and global relationships of data samples that are generated in real-world processes. In this research, we focus on a multi-scale kernel based technique named Auto-adaptive Laplacian Pyramids (ALP). This method can be useful for function approximation and interpolation. ALP is an extension of the standard Laplacian Pyramids model that incorporates a modified Leave-One-Out Cross Validation procedure, which makes the method stable and automatic in terms of parameters selection without extra cost. This paper introduces a new algorithm that extends ALP to fit datasets that are non-uniformly distributed. In particular, the optimal stopping criterion will be point-dependent with respect to the local noise level and the sample rate. Experimental results over real datasets highlight the advantages of the proposed multi-scale technique for modeling and learning complex, high dimensional data.

基于内核的技术已成为描述现实世界中生成的数据样本的局部和全局关系的一种常用方法。在这项研究中，我们专注于基于多尺度内核的技术，称为自适应拉普拉斯金字塔（ALP）。此方法对于函数逼近和插值很有用。ALP是标准拉普拉斯金字塔模型的扩展，该模型合并了修改后的“留一法”交叉验证程序，该程序使该方法在参数选择方面稳定且自动，无需额外费用。本文介绍了一种新算法，该算法扩展了ALP以适合非均匀分布的数据集。特别地，最佳停止标准将相对于局部噪声水平和采样率是点相关的。