Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization

2026-05-01

AI Summary

This work addresses the disconnect between graph drawing and dimensionality reduction in their optimization paradigms by proposing a stochastic gradient descent–based stress minimization method that systematically incorporates the local pairwise update strategy from graph drawing into high-dimensional data embedding. The approach unifies the optimization frameworks of these two tasks for the first time and is fully compatible with the scikit-learn estimator interface. Experimental results on standard high-dimensional benchmark datasets demonstrate that, compared to the classical SMACOF algorithm, the proposed method achieves significantly faster convergence while attaining comparable or lower stress values, thereby substantially improving visualization efficiency and scalability.

Abstract

Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on the SMACOF algorithm despite graph drawing results showing that simpler stochastic optimization schemes can be more effective for the same objective. We bridge these domains by adapting Stochastic Gradient Descent (SGD) techniques from graph drawing to vector data embedding. We present a scikit-learn compatible estimator that minimizes global stress through local pairwise updates, improving upon the existing implementation. Experiments on standard high-dimensional benchmarks show that our stochastic solver converges substantially faster than SMACOF while achieving comparable or lower stress.

Problem

• Graph Drawing
• Dimensionality Reduction
• Stress Optimization
• Multidimensional Scaling
• Stochastic Optimization

Innovation

• Stochastic Stress Optimization
• Graph Drawing
• Dimensionality Reduction
• Multidimensional Scaling
• Stochastic Gradient Descent