Abstract
We detail scalable methods for approximating the quadratic entropy $p^T d p$ for arbitrary distributions $p$ and common distances $d$ of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where $d$ is held constant while $p$ varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.
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- Green open access
Cite this article
APA 7
Huntsman, S. (2026). Efficient quadratic entropy with distance sketches. https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches
MLA 9
Huntsman, Steve. "Efficient quadratic entropy with distance sketches." https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches.
Chicago (author–date)
Huntsman, Steve. 2026. "Efficient quadratic entropy with distance sketches." https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches.
Harvard
Huntsman, S. (2026) 'Efficient quadratic entropy with distance sketches', Available at: https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches.
Vancouver
Huntsman S. Efficient quadratic entropy with distance sketches. https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches
IEEE
S. Huntsman, "Efficient quadratic entropy with distance sketches," https://omanscience.com/en/articles/efficient-quadratic-entropy-with-distance-sketches.