Adaptive Geometric Regression for High-Dimensional Structured Data
面向高维结构化数据的自适应几何回归
We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge in analyzing datasets with high ambient dimension but low intrinsic dimension, such as microbiome compositions, where traditional approaches fail to capture the underlying geometric structure. Starting from a k-nearest neighbor covering…