Related papers: Understanding and Improving UMAP with Geometric an…

Real-time crack segmentation is vital for structural health monitoring but is plagued by aleatoric uncertainties arising from varying lighting, blur, and texture ambiguity. Current uncertainty-aware approaches typically treat uncertainty…

A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…

Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications. However, the high computational cost of Wasserstein distance…

Image-to-3D models increasingly rely on hierarchical generation to disentangle geometry and texture. However, the design choices underlying these two-stage models--particularly the optimal choice of intermediate geometric…

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

This paper provides a fresh view of the neural network (NN) data flow problem, i.e., identifying the NN connections that are most important for the performance of the full model, through the lens of graph theory. Understanding the NN data…

Supervised mapping methods project multi-dimensional labeled data onto a 2-dimensional space attempting to preserve both data similarities and topology of classes. Supervised mappings are expected to help the user to understand the…

We introduce Uniform Manifold Approximation with Two-phase Optimization (UMATO), a dimensionality reduction (DR) technique that improves UMAP to capture the global structure of high-dimensional data more accurately. In UMATO, optimization…

Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…

In this letter we investigate a tightly coupled Lidar-Inertia Odometry and Mapping (LIOM) scheme, with the capability to incorporate multiple lidars with complementary field of view (FOV). In essence, we devise a time-synchronized scheme to…

High-confidence overlap prediction and accurate correspondences are critical for cutting-edge models to align paired point clouds in a partial-to-partial manner. However, there inherently exists uncertainty between the overlapping and…

Over the past decade, lidars have become a cornerstone of robotics state estimation and perception thanks to their ability to provide accurate geometric information about their surroundings in the form of 3D scans. Unfortunately, most of…

Vision-Language Models (VLMs) such as CLIP learn a shared embedding space for images and text, yet their representations remain geometrically separated, a phenomenon known as the modality gap. This gap limits tasks requiring cross-modal…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

Existing LiDAR-Inertial Odometry (LIO) methods typically utilize the prior trajectory derived from the IMU integration to compensate for the motion distortion within LiDAR frames. However, discrepancies between the prior and true trajectory…

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

Efficient UAV exploration in unknown environments requires rapid coverage expansion while maintaining accurate and reliable localization, since safe navigation in complex scenes depends on consistent mapping and pose estimation. However,…

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh…