Related papers: Euclidean Embedding of Data Using Local Distances

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited…

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…

We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…

Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…

Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to…

In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of…

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…

Lagrangian trajectories are widely used as observations for recovering the underlying flow field via Lagrangian data assimilation (DA). However, the strong nonlinearity in the observational process and the high dimensionality of the…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…

Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport…

Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…

Entity Resolution (ER) is a constitutional part for integrating different knowledge graphs in order to identify entities referring to the same real-world object. A promising approach is the use of graph embeddings for ER in order to…

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…

In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The…

Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node…