Stable Vectorization of Persistent Laplacians via Spectral Descriptors

Inkee Jung; Wonwoo Kang; Heehyun Park

Home/Archive/arXiv

arXiv · 2512.05463

Stable Vectorization of Persistent Laplacians via Spectral Descriptors

Inkee Jung·Wonwoo Kang·Heehyun Park

View original source ↗Read source document ↗Export metadata ↓

Abstract

Persistence images vectorize persistence diagrams into stable, finite-dimensional features. Inspired by this idea, we developed a vectorization framework for the spectral information encoded by the persistent Laplacian (PL). Given a scalar signature of a persistent Laplacian, we form a Persistent Laplacian Diagram (PLD) and smooth it into a Persistent Laplacian Image (PLI). We prove a stability theorem for PLIs with respect to the Wasserstein distance between PLDs under an admissibility condition on the signature. Through experiments on MNIST and QM7, we show that PLI with suitable signatures, especially the trace, provides an effective way to extract predictive topological and geometric information from PL, outperforming existing PL-based representations in these settings.

Explore related subjects

math.AT cs.CG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Inkee Jung, Wonwoo Kang, Heehyun Park. 2025-12-05. Stable Vectorization of Persistent Laplacians via Spectral Descriptors. https://arxiv.org/abs/2512.05463

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Homogeneous Milnor fibers and Kato--Matsumoto bounds via simplicial multiwedges

For every $n\geq 3$ and $s\geq 2$, we construct a homogeneous polynomial of degree $n(n+1)/2$ whose Milnor fiber is exactly $2s$-connected and whose rational cohomology contains a strictly defined nontrivial $n$-fold Massey product on classes of degree $2s+1$, implying that the Milnor fiber is non-formal, while attaining the Kato--Matsumoto connectivity bound. Our construction is based on the simplicial multiwedges of the nerve complexes of simple polytopes introduced by Limonchenko, combined with Suciu's realization of weighted homogeneous Milnor fibers. We thereby answer two problems posed by Suciu.

math.AT↗

arXiv2026

The homotopy types of directed path and trace spaces

We construct a saturated directed space with a Hausdorff $\Delta$-generated underlying space and two distinct points such that the trace space between them is homeomorphic to a square, whereas the directed path space has a nontrivial fundamental group. In particular, the canonical quotient map is not a weak homotopy equivalence. The same conclusion holds for regular directed paths modulo increasing homeomorphisms.

math.AT↗

arXiv2026

Moduli spaces of geometric functorial field theories

We develop tools to compute moduli spaces of geometric functorial field theories as mapping spaces of equivariant simplicial presheaves. Given a d-dimensional geometric structure F, presented as a presheaf on the site of smooth families of d-manifolds, we define its Cartesian realization, which is an O(d)-equivariant simplicial presheaf on the site of Cartesian spaces. We use Cartesian realizations to present the moduli space of functorial field theories with geometric structure F as a mapping space between O(d)-equivariant simplicial presheaves. In a companion paper, we use this result to compute the moduli space of smooth one-dimensional oriented Riemannian functorial field theories valued in an arbitrary smooth symmetric monoidal infinity-category.

math.AT↗