Related papers: On Epsilon-Nets, Distance Oracles, and Metric Embe…

A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…

Analyzing large-scale time-series network data, such as social media and email communications, poses a significant challenge in understanding social dynamics, detecting anomalies, and predicting trends. In particular, the scalability of…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

Low-dimensional node embeddings play a key role in analyzing graph datasets. However, little work studies exactly what information is encoded by popular embedding methods, and how this information correlates with performance in downstream…

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…

We study two aspects of information semantics: (i) the collection of all relationships, (ii) tracking and spotting anomaly and change. The first is implemented by endowing all relevant information spaces with a Euclidean metric in a common…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…

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…

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…

In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…

We introduce an orientation-preserving landmark-based distance for continuous curves, which can be viewed as an alternative to the \Frechet or Dynamic Time Warping distances. This measure retains many of the properties of those measures,…

In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…

We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any…

A variety of knowledge graph embedding approaches have been developed. Most of them obtain embeddings by learning the structure of the knowledge graph within a link prediction setting. As a result, the embeddings reflect only the structure…

We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…

The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…