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Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric…
Graph representation learning (also known as network embedding) has been extensively researched with varying levels of granularity, ranging from nodes to graphs. While most prior work in this area focuses on node-level representation,…
Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground…
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space $\mathbb{R}^d$ or on a sphere and which in addition satisfy certain edge length constraints. One of the major open problems in this field…
\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database.…
While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…