Related papers: GEFL: Extended Filtration Learning for Graph Class…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Graph neural networks (GNNs) are prominent for their effectiveness in processing graph data for semi-supervised node classification tasks. Most works of GNNs assume that the observed structure accurately represents the underlying node…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
The rise of graph-structured data has driven major advances in Graph Machine Learning (GML), where graph embeddings (GEs) map features from Knowledge Graphs (KGs) into vector spaces, enabling tasks like node classification and link…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
Graph learning (GL) can dynamically capture the distribution structure (graph structure) of data based on graph convolutional networks (GCN), and the learning quality of the graph structure directly influences GCN for semi-supervised…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Graph representation learning has emerged as a powerful tool for preserving graph topology when mapping nodes to vector representations, enabling various downstream tasks such as node classification and community detection. However, most…
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
Graph neural networks (GNNs) often struggle to learn discriminative node representations for heterophilic graphs, where connected nodes tend to have dissimilar labels and feature similarity provides weak structural cues. We propose…
Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended persistence module of the height function over that shape…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Subgraph pattern detection aims to uncover complex interaction structures in graphs. However, state-of-the-art graph neural network (GNN)-based solutions assume centralized access to the entire graph. When graphs are instead distributed…
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…
Slow feature analysis (SFA) is an unsupervised-learning algorithm that extracts slowly varying features from a multi-dimensional time series. A supervised extension to SFA for classification and regression is graph-based SFA (GSFA). GSFA is…
Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…