Beyond Normal: Learning Spatial Density Models of Node Mobility

TL;DR

This paper explores modeling the steady-state spatial density of mobile nodes on a 2D terrain using mixture models, proposing M"obius distributions for better symmetry and flexibility, but noting challenges in learning mixtures of M"obius distributions.

Contribution

It introduces M"obius distributions for spatial density modeling and compares them with Gaussian mixtures, highlighting their advantages and learning difficulties.

Findings

M"obius distributions better capture symmetric spatial relations.

Mixture models with M"obius distributions outperform Gaussian mixtures in flexibility.

Learning mixtures of M"obius distributions is more fragile with current tools.

Abstract

Learning models of complex spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain, can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability for off-the-shelf mixture density network models for the description of mobile node density over a disk. We propose the use of M\"obius distributions to retain symmetric spatial relations, yet be flexible enough to capture changes as one radially traverses the disk. The mixture models for M\"obius versus Gaussian distributions are compared and the benefits of choosing M\"obius distributions become evident, yet we also observe that learning mixtures of M\"obius distributions is a fragile process, when using current tools, compared to learning mixtures of Gaussians.