Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization

TL;DR

This paper introduces a stochastic optimization method for dimensionality reduction that accelerates convergence compared to traditional algorithms, bridging the gap between graph drawing and DR.

Contribution

It adapts stochastic gradient descent techniques from graph drawing to vector data embedding, resulting in faster convergence and improved performance.

Findings

Stochastic solver converges faster than SMACOF.

Achieves comparable or lower stress on benchmarks.

Provides a scikit-learn compatible implementation.

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.