Related papers: GeodesicEmbedding (GE): A High-Dimensional Embeddi…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…

We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…

In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…

Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation…

Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables…

In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…

Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…

We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here,…

A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically…

While 3D Gaussian Splatting has achieved remarkable success in photorealistic novel view synthesis, its pursuit of fast and high-fidelity 3D reconstruction has long been constrained by a trade-off between geometric accuracy and optimization…

We study the image-based geolocalization problem, aiming to localize ground-view query images on cartographic maps. Current methods often utilize cross-view localization techniques to match ground-view query images with 2D maps. However,…

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…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar…

In the current deep learning based recommendation system, the embedding method is generally employed to complete the conversion from the high-dimensional sparse feature vector to the low-dimensional dense feature vector. However, as the…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…