M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation

Nicholas Chia; Junji Nakano

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arXiv · 0802.1669

M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation

Nicholas Chia·Junji Nakano

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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.

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Nicholas Chia, Junji Nakano. 2010-04-21. M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation. https://arxiv.org/abs/0802.1669

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