Related papers: Towards an Optimal Bound for the Interleaving Dist…

Graph embedding techniques allow to learn high-quality feature vectors from graph structures and are useful in a variety of tasks, from node classification to clustering. Existing approaches have only focused on learning feature vectors for…

Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…

We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved…

Successful machine learning on graphs or networks requires embeddings that not only represent nodes and edges as low-dimensional vectors but also preserve the graph structure. Established methods for generating embeddings require flexible…

Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…

Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…

Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…

The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations.…

Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…

Graph machine learning has enjoyed a meteoric rise in popularity since the introduction of deep learning in graph contexts. This is no surprise due to the ubiquity of graph data in large scale industrial settings. Tacitly assumed in all…

We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…

Distance-based outlier detection is widely adopted in many fields, e.g., data mining and machine learning, because it is unsupervised, can be employed in a generic metric space, and does not have any assumptions of data distributions. Data…

Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…

GNNs have been proven to perform highly effective in various node-level, edge-level, and graph-level prediction tasks in several domains. Existing approaches mainly focus on static graphs. However, many graphs change over time with their…

Graph similarity is critical in graph-related tasks such as graph retrieval, where metrics like maximum common subgraph (MCS) and graph edit distance (GED) are commonly used. However, exact computations of these metrics are known to be…

As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…

Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…

Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…