arXiv:2607. 16178v1 Announce Type: cross Abstract: In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure.
arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.
arXiv:2609.26748v1 Announce Type: cross Abstract: Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters,...
Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion. However, minimizing transport cost or distortion alone may fail to identify a geometrically meaningful transformation between the two distributions.
The paper introduces CluProp, a framework that treats varied‑density clustering in high‑dimensional spaces as a label propagation process over neighborhood graphs. By combining density‑based ideas with graph connectivity, it offers a deterministic propagation strategy that reduces parameter sensitivity and scales efficiently to millions of points. CluProp is agnostic to distance metrics and consistently outperforms existing baselines in accuracy while processing large datasets in minutes.
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
arXiv:2608. 19783v1 Announce Type: new Abstract: Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion.
arXiv:2606. 08258v1 Announce Type: cross Abstract: Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison.
arXiv:2607. 24237v1 Announce Type: new Abstract: Many existing clustering methods are designed based on a set-oriented definition---a cluster is a set of similar points---relying a point-to-point similarity function to find similar points.
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
The paper introduces LA-VDM, a landmark‑constrained algorithm that speeds up Vector Diffusion Maps (VDM) by employing a two‑stage normalization to handle nonuniform sampling in both data and landmark sets. It demonstrates that, under a manifold model with a frame bundle structure, LA‑VDM can accurately recover parallel transport from a point cloud and asymptotically converges to the connection Laplacian. Experiments on simulated data and a nonlocal image denoising application confirm the method’s performance and accuracy.
arXiv:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.