Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization

• URL: http://arxiv.org/abs/2605.00641v1
• Date: Fri, 01 May 2026 13:22:56 GMT
• Title: Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization
• Abstract summary: Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms.<n>We bridge these domains by adapting Gradient Descent (SGD) techniques from graph drawing to vector data embedding.
• Score: 0.22940141855172028
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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