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We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo…

Learning High-Resolution representations is essential for semantic segmentation. Convolutional neural network (CNN)architectures with downstream and upstream propagation flow are popular for segmentation in medical diagnosis. However, due…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Faraday complexity describes whether a spectropolarimetric observation has simple or complex magnetic structure. Quickly determining the Faraday complexity of a spectropolarimetric observation is important for processing large, polarised…

Temporal graph clustering is a complex task that involves discovering meaningful structures in dynamic graphs where relationships and entities change over time. Existing methods typically require centralized data collection, which poses…

How can we expand the tensor decomposition to reveal a hierarchical structure of the multi-modal data in a self-adaptive way? Current tensor decomposition provides only a single layer of clusters. We argue that with the abundance of…

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive…

Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion…

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…

Cluster analysis plays a very important role in data analysis. In these years, cluster ensemble, as a cluster analysis tool, has drawn much attention for its robustness, stability, and accuracy. Many efforts have been done to combine…

Document structure extraction has been a widely researched area for decades with recent works performing it as a semantic segmentation task over document images using fully-convolution networks. Such methods are limited by image resolution…

Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…

Designing a network to learn a molecule structure given its physical/chemical properties is a hard problem, but is useful for drug discovery tasks. In this paper, we incorporate higher-order relational learning of Factor Graphs with strong…

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…

Driven by the growth of Web-scale decentralized services, Federated Clustering (FC) aims to extract knowledge from heterogeneous clients in an unsupervised manner while preserving the clients' privacy, which has emerged as a significant…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…

Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…

A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression…

Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…

Classification with Costly Features (CwCF) is a classification problem that includes the cost of features in the optimization criteria. Individually for each sample, its features are sequentially acquired to maximize accuracy while…