M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation
Methodology
2010-04-22 v2 Statistics Theory
Machine Learning
Statistics Theory
Abstract
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-decomposable density via a mixture of unimodal densities. Finally, we demonstrate the application of M-decomposability to clustering and kernel density estimation, using real and simulated data. Our results show that M-decomposability can be used as a non-parametric criterion to locate modes in probability densities.
Cite
@article{arxiv.0802.1669,
title = {M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation},
author = {Nicholas Chia and Junji Nakano},
journal= {arXiv preprint arXiv:0802.1669},
year = {2010}
}
Comments
30 pages, 13 figures