arXiv:2606. 06505v1 Announce Type: cross Abstract: We introduce a user defined probabilistic polygonal representation for plane curves.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.
arXiv:2607. 19600v1 Announce Type: cross Abstract: The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.
arXiv:2603. 09793v2 Announce Type: replace Abstract: Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions.
arXiv:2606. 00139v1 Announce Type: cross Abstract: Curvature-penalized geodesic models have proven their effectiveness in image segmentation by computing globally optimal curves.
The paper introduces a pullback Riemannian geometry tailored for multimodal data by employing a latent Gaussian mixture model. It defines a smooth, positive‑definite metric based on responsibility‑weighted component precision, extending the standard single‑Gaussian construction. Experiments on synthetic, multi‑view image, and MNIST datasets demonstrate reduced transport distortion, accurate trajectory recovery, and more realistic interpolation.
arXiv:2607. 03112v1 Announce Type: cross Abstract: We revisit random projections for reducing the dimension of high-dimensional polygonal curves.
The paper introduces a new representation‑adaptive kernel class that, on a fixed sample, yields a union of reproducing‑kernel Hilbert‑space ellipsoids instead of a single ellipsoid. It defines a minimum‑trace common covariance dominating the empirical union generated by Brownian kernel ladders, and derives exact formulations, statistical and computational consequences, and a universal Gaussian‑complexity bound. The work further develops geometric reductions, deterministic depth laws, and exact empirical Kolmogorov‑width formulas, providing both lower and upper certificates for covariance certification and illustrating the distinction between successful covariance certification and predictive selection.