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:2601. 20844v3 Announce Type: replace-cross Abstract: This paper studies the Minimal Embeddable Dimension (MED): the least dimension in which there exists a configuration of $m$ object vectors so that every subset of size at most $k$ is exactly retrieved by score comparison.
arXiv:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
arXiv:2601. 09173v5 Announce Type: replace Abstract: Representational similarity analysis and related methods compare the internal geometries of neural networks, but they measure only alignment between spaces, leaving a blind spot -- whether a representation's structure is reliably recoverable, not merely similar.
DMT‑Dens is a parametric manifold‑visualization technique that uses a latent‑token Transformer encoder to produce two‑dimensional embeddings of high‑dimensional biological data. It preserves sampling density by aligning rank‑based manifold structures and optimizing a Pearson‑correlation loss on k‑nearest‑neighbor log‑radius estimates. Benchmark tests show that DMT‑Dens maintains density fidelity while achieving competitive label separability on biological datasets.
arXiv:2608. 15632v1 Announce Type: cross Abstract: Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret.
arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
arXiv:2406. 07049v3 Announce Type: replace-cross Abstract: Understanding spatial relationships across all dimensions is fundamental for intelligent systems.
The paper introduces the Rashomon set for dimension reduction, a collection of equally good embeddings that preserve high‑dimensional structure. It proposes PCA‑informed alignment to make axes interpretable, concept‑alignment regularization to incorporate external knowledge, and a method to extract trustworthy nearest‑neighbor relationships across the Rashomon set for refined embeddings. These techniques aim to produce interpretable, robust, and goal‑aligned visualizations by leveraging multiple valid embeddings instead of a single one.
The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive.
arXiv:2604. 13230v2 Announce Type: replace Abstract: Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems.