The paper introduces Hypersolid, a self‑supervised learning objective that uses short‑range repulsion to prevent representation collapse. It combines view alignment with local collision avoidance, creating a latent geometry of compact, semantically aligned neighborhoods with low anisotropy. This geometry improves unsupervised clustering and fine‑grained separation, though it reduces transferability.
arXiv:2606. 04451v1 Announce Type: new Abstract: Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space.
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:2509. 03373v2 Announce Type: replace Abstract: Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure.
arXiv:2608.29867v1 Announce Type: new Abstract: Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear enc...
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:2510. 15141v5 Announce Type: replace-cross Abstract: Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration.
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.
Combinatorial Network-Based Manifold Topological Deep Learning (CNMTDL) is a new framework that represents medical images as discrete manifolds and decomposes them into three Hodge components. Features from these components are concatenated and fed into a combinatorial complex architecture, enabling higher‑order message passing between 0‑cells and 2‑cells via attention‑based blocks. CNMTDL was evaluated on six 2D and 3D datasets from the MedMNIST v2 benchmark, showing improved performance for medical image analysis.
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:2610.33872v1 Announce Type: cross Abstract: Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geo...
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) is a geometry-driven framework that adapts the spatial support of each neighborhood based on local geometric complexity. It estimates intrinsic dimensionality with TwoNN, builds an intrinsic representation via PCA, and uses a shape-operator-based estimate of local mean curvature to shrink the radius in highly curved regions while keeping a broader support in flatter areas. Experiments on over 70 OpenML datasets show that CARSANN consistently outperforms standard k‑NN and rivals other adaptive nearest‑neighbor methods, achieving a mean balanced accuracy increase from 0.6506 to 0.7528 and statistically significant improvements on most datasets.