Jacob Miller

Ya Ji, Xuefeng Li, Timo Brand et al.

Graphs are commonly visualized in 2D, where humans readily interpret spatial relationships, yet such layouts often distort higher-dimensional structure. We propose to embed graphs in high-dimensional space and search for informative 2D viewpoints that optimize aesthetic and readability metrics (e.g., edge crossings and angular resolution), enabled by a novel differentiable surrogate for edge crossings. Numerical experiments show that these viewpoints consistently outperform standard 2D layouts, and can even surpass methods explicitly designed to optimize these metrics. We further introduce DataFly, an interactive system for exploring multiple candidate viewpoints through seamless navigation. A usability study demonstrates that our approach reveals structural patterns that remain hidden in conventional 2D visualizations.

Daniel Hangan, Stephen Kobourov, Jacob Miller

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.

Kaviru Gunaratne, Stephen Kobourov, Jacob Miller

Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure clusters while local methods can over-emphasize them. Yet, even when clusters appear distinct, their relative arrangement in the projection may be arbitrary or misleading, a common issue in techniques such as t-SNE and UMAP. Existing cluster quality metrics either only measure cluster separability or assume spherical, globular clusters in the original space. We introduce the Class Angular Distortion Index (CADI), a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection. We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result. Since it relies on computing angles, CADI is also differentiable, enabling optimization. We demonstrate this with a CADI-based DR technique.