Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization

arXiv cs.LG / 5/4/2026

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Key Points

The paper proposes a connection between dimensionality reduction (DR) and graph drawing (GD) by rethinking their optimization approaches, highlighting that stochastic methods can outperform SMACOF in related settings.
It adapts stochastic gradient descent (SGD) techniques from graph drawing to vector-based embedding, targeting minimization of global stress via local pairwise updates.
The authors release a scikit-learn compatible estimator that improves on an existing implementation while keeping the same objective of global stress minimization.
Experiments on common high-dimensional benchmarks indicate that the new stochastic solver converges significantly faster than SMACOF while reaching comparable or lower stress values.

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.