Related papers: On Epsilon-Nets, Distance Oracles, and Metric Embe…
Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…
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…
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These…
Ontology matching is a core task when creating interoperable and linked open datasets. In this paper, we explore a novel structure-based mapping approach which is based on knowledge graph embeddings: The ontologies to be matched are…
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…
Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
An inverse modeling technique is introduced that combines elements of coupled logistic map models and wavelet analysis for the purpose of analyzing partial synchronization states in high-dimensional systems. Using Embedded Complex Logistic…
Information networks are ubiquitous and are ideal for modeling relational data. Networks being sparse and irregular, network embedding algorithms have caught the attention of many researchers, who came up with numerous embeddings algorithms…
We study deterministic online embeddings of metrics spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces,…
Deep metric learning aims to learn an embedding space where the distance between data reflects their class equivalence, even when their classes are unseen during training. However, the limited number of classes available in training…
We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis…
Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
Numerous works have proven that existing neighbor-averaging Graph Neural Networks cannot efficiently catch structure features, and many works show that injecting structure, distance, position or spatial features can significantly improve…
Long-range dependencies are critical for effective graph representation learning, yet most existing datasets focus on small graphs tailored to inductive tasks, offering limited insight into long-range interactions. Current evaluations…
Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of 'events', or timestamped interactions, such as email and social media…