相关论文: Ground Metric Learning

The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…

Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…

The Gromov-Hausdorff (GH) distance is traditionally used for measuring distances between metric spaces. It is defined as the minimal distortion of embedding one surface into the other, while the optimal correspondence can be described as…

Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values…

This paper proposes a novel method for geo-tracking, i.e. continuous metric self-localization in outdoor environments by registering a vehicle's sensor information with aerial imagery of an unseen target region. Geo-tracking methods offer…

Our goal is to recognize material categories using images and geometry information. In many applications, such as construction management, coarse geometry information is available. We investigate how 3D geometry (surface normals, camera…

This paper focuses on pose registration of different object instances from the same category. This is required in online object mapping because object instances detected at test time usually differ from the training instances. Our approach…

Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear…

The goal of metric learning is to learn a function that maps samples to a lower-dimensional space where similar samples lie closer than dissimilar ones. Particularly, deep metric learning utilizes neural networks to learn such a mapping.…

Realistic metric spaces (such as road/transportation networks) tend to be much more algorithmically tractable than general metrics. In an attempt to formalize this intuition, Abraham et~al.\ (SODA 2010, JACM 2016) introduced the notion of…

The calculation of shortest-path distances in road networks is a core operation in navigation systems, location-based services, and spatial analytics. Although classical algorithms, e.g., Dijkstra's algorithm, provide exact answers, their…

Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…

Although haptic sensing has recently been used for legged robot localization in extreme environments where a camera or LiDAR might fail, the problem of efficiently representing the haptic signatures in a learned prior map is still open.…

Deep metric learning aims at learning the distance metric between pair of samples, through the deep neural networks to extract the semantic feature embeddings where similar samples are close to each other while dissimilar samples are…

Long-term metric self-localization is an essential capability of autonomous mobile robots, but remains challenging for vision-based systems due to appearance changes caused by lighting, weather, or seasonal variations. While…

Most of metric learning approaches are dedicated to be applied on data described by feature vectors, with some notable exceptions such as times series, trees or graphs. The objective of this paper is to propose a metric learning algorithm…

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…

The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…