arXiv:2608. 11269v1 Announce Type: cross Abstract: Omics datasets, particularly single-cell RNA sequencing data, are high-dimensional, sparse, noisy, and dominated by zero values, making faithful low-dimensional representation challenging.
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. 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:2605. 23540v2 Announce Type: replace Abstract: Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data.
arXiv:2608. 05336v1 Announce Type: cross Abstract: Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships.
arXiv:2607. 19387v1 Announce Type: cross Abstract: Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields.
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
NEST is an unsupervised framework that learns a single embedding encoding coarse‑to‑fine cluster structure, optimizing clustering and separation across nested prefix subspaces. The method uses rank and within‑cluster regularization to prevent collapse, and distances in the embedding align more closely with the true hierarchy than the input distances, even though the hierarchy is not provided during training. Experiments on synthetic, vision, text, and single‑cell data show that NEST can recover multiscale structure given only the number of clusters per level, demonstrating its ability to discover multiscale organization in real‑world representations.
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
The paper introduces an unsupervised framework that merges manifold learning with rank‑based interpretable graph embeddings to address the Geometric and Interpretability Gaps in visual representation learning. By first analyzing contextual information on the dataset manifold and then producing sparse, self‑explainable embeddings, the method achieves dimensionality reduction while preserving or improving performance in image retrieval and semi‑supervised Graph Convolutional Network classification. Experiments across varied datasets confirm that these context‑aware representations maintain high downstream effectiveness.
arXiv:2607. 08746v1 Announce Type: cross Abstract: While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally.
arXiv:2601.20173v3 Announce Type: replace Abstract: We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervis...