Related papers: Spectral embedding of weighted graphs
Despite much research, Graph Neural Networks (GNNs) still do not display the favorable scaling properties of other deep neural networks such as Convolutional Neural Networks and Transformers. Previous work has identified issues such as…
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
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…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
Spectral embedding provides a framework for solving perceptual organization problems, including image segmentation and figure/ground organization. From an affinity matrix describing pairwise relationships between pixels, it clusters pixels…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
Attention networks have proven to be an effective approach for embedding categorical inference within a deep neural network. However, for many tasks we may want to model richer structural dependencies without abandoning end-to-end training.…
This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a general and more realistic setup. Specifically, the comparison graph…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can…
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…
We argue that Transformers are essentially graph-to-graph models, with sequences just being a special case. Attention weights are functionally equivalent to graph edges. Our Graph-to-Graph Transformer architecture makes this ability…