Document Type
Article
Publication Date
12-16-2013
Abstract
Given a set of data W={w1,…,wN}∈RD drawn from a union of subspaces, we focus on determining a nonlinear model of the form U=⋃i∈ISi, where {Si⊂RD}i∈I is a set of subspaces, that is nearest to W. The model is then used to classify W into clusters. Our approach is based on the binary reduced row echelon form of data matrix, combined with an iterative scheme based on a non-linear approximation method. We prove that, in absence of noise, our approach can find the number of subspaces, their dimensions, and an orthonormal basis for each subspace Si. We provide a comprehensive analysis of our theory and determine its limitations and strengths in presence of outliers and noise.
Recommended Citation
Akram Aldroubi, Ali Sekmen, "Reduced row echelon form and non-linear approximation for subspace segmentation and high-dimensional data clustering", Applied and Computational Harmonic Analysis, Volume 37, Issue 2, 2014, Pages 271-287, ISSN 1063-5203, https://doi.org/10.1016/j.acha.2013.12.001.