Geometric multi-resolution analysis based classification for high dimensional data

Abstract

Data sets are often modeled as point clouds lying in a high dimensional space. In practice, they usually reside on or near a much lower dimensional manifold embedded in the ambient space; this feature allows for both a simple representation of the data as well as accurate performance for statistical inference procedures such as estimation, regression and classification. In this paper we propose a framework based on geometric multi-resolution analysis (GMRA) to tackle the problem of classifying data lying around a low-dimensional set M embedded in a high-dimensional space R$^textrmD$. We test our algorithms on real data sets and demonstrate its efficacy in the presence of noise.