Euclidean Embedding of the Poisson Weighted Infinite Tree and Application to Mobility Models

TL;DR

This paper explores Euclidean embeddings of Poisson weighted infinite trees derived from continuous time branching models, and applies these to model and analyze human and animal mobility patterns.

Contribution

It introduces a novel Euclidean embedding framework for Poisson weighted infinite trees and demonstrates their application in modeling mobility behaviors.

Findings

Effective modeling of mobility patterns using the proposed Euclidean embeddings.

Controlled Hausdorff dimension allows for flexible fractal modeling.

Application to real-world mobility data shows promising results.

Abstract

Continuous time branching models are used to create random fractals in a Euclidean space, whose Hausdorff dimension is controlled by an input parameter. Finite realizations are applied in modelling the set of sites visited in models of human and animal mobility.