Related papers: Link Prediction with Persistent Homology: An Inter…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…
Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node…
In machine-learning-assisted high-throughput defect studies, a defect-aware latent representation of the supercell structure is crucial to the accurate prediction of defect properties. The performance of current graph neural network (GNN)…
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…
Link prediction is an important task that has wide applications in various domains. However, the majority of existing link prediction approaches assume the given graph follows homophily assumption, and designs similarity-based heuristics or…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
Link prediction is a classical problem in graph analysis with many practical applications. For directed graphs, recently developed deep learning approaches typically analyze node similarities through contrastive learning and aggregate…
Link prediction aims to estimate the likelihood of connections between pairs of nodes in complex networks, which is beneficial to many applications from friend recommendation to metabolic network reconstruction. Traditional heuristic-based…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Bipartite networks serve as highly suitable models to represent systems involving interactions between two distinct types of entities, such as online dating platforms, job search services, or ecommerce websites. These models can be…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
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…
Inductive link prediction with knowledge hypergraphs is the task of predicting missing hyperedges involving completely novel entities (i.e., nodes unseen during training). Existing methods for inductive link prediction with knowledge…