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Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…

Recently, there has been an emerging trend to integrate persistent homology (PH) into graph neural networks (GNNs) to enrich expressive power. However, naively plugging PH features into GNN layers always results in marginal improvement with…

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features…

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…

Graph representation learning (GRL) is a fundamental task in machine learning, aiming to encode high-dimensional graph-structured data into low-dimensional vectors. Self-supervised learning (SSL) methods are widely used in GRL because they…

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…

Biomedical networks (or graphs) are universal descriptors for systems of interacting elements, from molecular interactions and disease co-morbidity to healthcare systems and scientific knowledge. Advances in artificial intelligence,…

Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous…

Graphs representation learning has been a very active research area in recent years. The goal of graph representation learning is to generate graph representation vectors that capture the structure and features of large graphs accurately.…

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…

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,…

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

In recent years, Hypergraph Neural Networks (HNNs) have demonstrated immense potential in handling complex systems with high-order interactions. However, acquiring large-scale, high-quality labeled data for these models is costly, making…

While representation learning has yielded a great success on many graph learning tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if the topological features,…

Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…

In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph…

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…

Continual learning on graphs tackles the problem of training a graph neural network (GNN) where graph data arrive in a streaming fashion and the model tends to forget knowledge from previous tasks when updating with new data. Traditional…