Geometric Learning and Finsler Metrics in Weighted Projective Spaces

Tanush Shaska

I-AIMS paper sh-97 · Published in Adv. Pure Appl. Math. 17 (2026), no. 3, 29–54 · 2026

This paper develops a hierarchical clustering algorithm for weighted projective spaces ℙ_q, utilizing a Finsler metric d_F([z], [w]) and its rational analogue d_(F,ℚ)([z], [w]) to define distances that preserve the non-Euclidean geometry of these quotient manifolds. Defined via geodesic integrals of a scaling-invariant Finsler norm weighted by the grades q = (q₀, q₁, …, qₙ), these metrics satisfy true metric properties—including the triangle inequality—overcoming the limitations of the non-metric dissimilarity measure from prior work.

MSC classes: 53C60

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References

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