TL;DR本文证明了新型 k 近邻自适应带宽核的 Laplacian 算子收敛至流形加权 Laplacian,并支持该理论结果通过在模拟数据和手写数字图像数据上进行的数值实验。
Abstract
kernelized gram matrix $W$ constructed from data points $\{x_i\}_{i=1}^N$ as $W_{ij}= k_0( \frac{ \| x_i - x_j \|^2} {\sigma^2} ) $ is widely used in graph-based geometric data analysis and unsupervised learning.