Enhanced Force-Scheme: A fast and accurate global dimensionality reduction method
Jaume Ros, Alessio Arleo, Fernando V. Paulovich · Computers & Graphics · 2026
Global nonlinear Dimensionality Reduction (DR) methods excel at capturing complex features of datasets while preserving their overall high-dimensional structure when projecting them into a lower-dimensional space. Force-Scheme (FS) is one such method, used in a variety of domains. However, its use is still hindered by distortions and high computational cost. In this paper, we introduce Enhanced Force-Scheme (EFS), a revisited approach to solve the optimization problem posed by FS. We build on the core ideas of the original FS algorithm and introduce a more advanced optimization framework grounded in gradient-based optimization, which yields higher-quality layouts. Additionally, we elaborate on multiple strategies to accelerate the computation of projections using EFS, thereby facilitating its use on large datasets. Finally, we compare it with FS and other popular DR techniques and show that, among the methods tested, EFS best captures global structure while still performing well on local metrics. • Presentation of a new model (Enhanced Force-Scheme, EFS) that corrects major artifacts in Force-Scheme (FS) layouts by rethinking the way in which points are moved during the optimization. • Introduction of gradient descent concepts to obtain more reliable convergence and more detail in the resulting layouts. • Introduction of multiple strategies for scaling EFS and enable the projection of large datasets.