相关论文: Representing higher-order dependencies in networks

Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations…

A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…

Convolutional Neural Networks (CNNs) have revolutionized the understanding of visual content. This is mainly due to their ability to break down an image into smaller pieces, extract multi-scale localized features and compose them to…

In-service structural health monitoring is a so far rarely exploited, yet potent option for early-stage crack detection and identification in train wheelset axles. This procedure is non-trivial to enforce on the basis of a purely…

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…

The inference of rankings plays a central role in the theory of social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based…

Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…

Temporal Graph Neural Networks (TGNNs) have gained growing attention for modeling and predicting structures in temporal graphs. However, existing TGNNs primarily focus on pairwise interactions while overlooking higher-order structures that…

Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…

Higher-order representations (HORs) are neural or computational states that are "about" first-order representations (FORs), encoding information not about the external world per se but about the agent's own representational processes --…

The present paper provides a generalized model of network, namely, Hybrid Layered Network (HLN). We proved that the sets of all homogeneous, heterogeneous and multi-layered networks are subsets of the set of all HLNs depicting the model's…

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…

Various deep neural network architectures (DNNs) maintain massive vital records in computer vision. While drawing attention worldwide, the design of the overall structure lacks general guidance. Based on the relationship between DNN design…

User response prediction makes a crucial contribution to the rapid development of online advertising system and recommendation system. The importance of learning feature interactions has been emphasized by many works. Many deep models are…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Dynamic systems that consist of a set of interacting elements can be abstracted as temporal networks. Recently, higher-order patterns that involve multiple interacting nodes have been found crucial to indicate domain-specific laws of…

We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…