Related papers: Visualizing the geometry of labeled high-dimension…

Dimensionality reduction of spatial omic data can reveal shared, spatially structured patterns of expression across a collection of genomic features. We study strategies for discovering and interactively visualizing low-dimensional…

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…

Visual relocalization, which estimates the 6-degree-of-freedom (6-DoF) camera pose from query images, is fundamental to remote sensing and UAV applications. Existing methods face inherent trade-offs: image-based retrieval and pose…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and geometry to…

We propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…

Most Gaussian Splatting techniques that provide a 3D semantic representation of the scene do not optimize the underlying 3D geometry, making object-level editing or asset extraction challenging. Recent methods, such as COBGS, Trace3D,…

Generating learning-friendly representations for points in a 2D space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec) were proposed to directly encode any point in…

Understanding complex scenes at multiple levels of abstraction remains a formidable challenge in computer vision. To address this, we introduce Nested Neural Feature Fields (N2F2), a novel approach that employs hierarchical supervision to…

3D Gaussian Splatting (3DGS) has emerged as a novel explicit representation for 3D scenes, offering both high-fidelity reconstruction and efficient rendering. However, 3DGS lacks 3D segmentation ability, which limits its applicability in…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However,…

Enforcing universal symmetries in machine learning (ML) models is a common strategy to mitigate data scarcity. We show that exploiting exact, as well as approximate, label symmetries can benefit scaling laws. We illustrate the idea for the…

The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…

To what extent is it possible to visualize high-dimensional data in two- or three-dimensional plots? We reframe this question in terms of embedding $n$-vertex graphs (representing the neighborhood structure of the input points) into metric…

In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…

Semantic segmentation requires a holistic understanding of the physical world, as it assigns semantic labels to spatially continuous and structurally coherent objects rather than to isolated pixels. However, existing data-free knowledge…