Friedrich Pagenkopf | Searcharxiv

arXiv2026

Nonlinear Dimensionality Reduction with Diffusion Maps in Practice

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones.

cs.LG↗

arXiv2021

Obscuring digital route choice information prevents delay-induced congestion

Although routing applications increasingly affect individual mobility choices, their impact on collective traffic dynamics remains largely unknown. Smart communication technologies provide accurate traffic data for choosing one route over other alternatives, yet inherent delays undermine the potential usefulness of such information. Here we introduce and analyze a simple model of collective traffic dynamics which result from route choice relying on outdated traffic information. We find for sufficiently small information delays that traffic flows are stable against perturbations. However, delays beyond a bifurcation point induce self-organized flow oscillations of increasing amplitude -- congestion arises. Providing delayed information averaged over sufficiently long periods of time or, more intriguingly, reducing the number of vehicles adhering to the route recommendations may prevent such delay-induced congestion. We reveal the fundamental mechanisms underlying these phenomena in a minimal two-road model and demonstrate their generality in microscopic, agent-based simulations of a road network system. Our findings provide a way to conceptually understand system-wide traffic dynamics caused by broadly used non-instantaneous routing information and suggest how resulting unintended collective traffic states could be avoided.

physics.soc-ph↗