Related papers: Persistent Homology and Graphs Representation Lear…
Graph embedding techniques, which learn low-dimensional representations of a graph, are achieving state-of-the-art performance in many graph mining tasks. Most existing embedding algorithms assign a single vector to each node, implicitly…
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,…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
Representation learning in dynamic graphs is a challenging problem because the topology of graph and node features vary at different time. This requires the model to be able to effectively capture both graph topology information and…
Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…
Financial transactions can be considered edges in a heterogeneous graph between entities sending money and entities receiving money. For financial institutions, such a graph is likely large (with millions or billions of edges) while also…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
We investigate the pertinence of methods from algebraic topology for text data analysis. These methods enable the development of mathematically-principled isometric-invariant mappings from a set of vectors to a document embedding, which is…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly-understood. In this paper we study a rich homology-based invariant first defined by Dey, Shi,…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
The complexity and non-Euclidean structure of graph data hinder the development of data augmentation methods similar to those in computer vision. In this paper, we propose a feature augmentation method for graph nodes based on topological…
Dynamic graph representation learning is a task to learn node embeddings over dynamic networks, and has many important applications, including knowledge graphs, citation networks to social networks. Graphs of this type are usually…
Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
Knowledge graphs have garnered significant research attention and are widely used to enhance downstream applications. However, most current studies mainly focus on static knowledge graphs, whose facts do not change with time, and disregard…