arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
arXiv:2608. 04234v1 Announce Type: cross Abstract: We study the problem of aligning data from multiple modalities into a shared representation space, focusing on settings where strong pretrained unimodal encoders are available but cross-modal paired data are scarce.
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
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:2608. 17571v1 Announce Type: cross Abstract: Motivation: Low-dimensional embeddings are widely used to explore cell-state heterogeneity in single-cell and other high-dimensional biological data.
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
arXiv:2607. 06583v1 Announce Type: cross Abstract: DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging.
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.