Related papers: Frequent subgraph-based persistent homology for gr…

Graph convolutional networks (GCNs) have recently enabled a popular class of algorithms for collaborative filtering (CF). Nevertheless, the theoretical underpinnings of their empirical successes remain elusive. In this paper, we endeavor to…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…

Standard Federated Learning (FL) techniques are limited to clients with identical network architectures. This restricts potential use-cases like cross-platform training or inter-organizational collaboration when both data privacy and…

The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…

Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…

Persistent homology (PH) is a powerful mathematical method to automatically extract relevant insights from images, such as those obtained by high-resolution imaging devices like electron microscopes or new-generation telescopes. However,…

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…

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)…

Graph Neural Networks have become one of the indispensable tools to learn from graph-structured data, and their usefulness has been shown in wide variety of tasks. In recent years, there have been tremendous improvements in architecture…

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,…

A machine learning (ML) feature network is a graph that connects ML features in learning tasks based on their similarity. This network representation allows us to view feature vectors as functions on the network. By leveraging function…

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the…

Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…

Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for…

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…

Graph Neural Networks (GNNs) have demonstrated strong capabilities in processing structured data. While traditional GNNs typically treat each feature dimension equally during graph convolution, we raise an important question: Is the graph…