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Fine-grained visual classification can be addressed by deep representation learning under supervision of manually pre-defined targets (e.g., one-hot or the Hadamard codes). Such target coding schemes are less flexible to model inter-class…
Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph…
We study d-dimensional generalizations of three mutually related topics in graph theory: Hamiltonian paths, (unit) interval graphs, and binomial edge ideals. We provide partial high-dimensional generalizations of Ore and Posa's sufficient…
Among other things, it is shown that for every pair of positive integers $r$, $d$, satisfying $1<r<d\leq 2r$, and every finite simple graph $H,$ there is a connected graph $G$ with diameter $d$, radius $r$, and center $H.$
This paper proposes a novel heterogeneous grid convolution that builds a graph-based image representation by exploiting heterogeneity in the image content, enabling adaptive, efficient, and controllable computations in a convolutional…
Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called…
We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and…
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…
Configuration space integrals are powerful tools for studying the homotopy type of the space of long embeddings in terms of a combinatorial object called a graph complex. It is unknown whether these integrals give a cochain map due to…
Important advances have been made using convolutional neural network (CNN) approaches to solve complicated problems in areas that rely on grid structured data such as image processing and object classification. Recently, research on graph…
Graph clustering aims to divide the graph into different clusters. The recently emerging deep graph clustering approaches are largely built on graph neural networks (GNN). However, GNN is designed for general graph encoding and there is a…
Graph Convolutional Network (GCN) has exhibited remarkable potential in improving graph-based clustering. To handle the general clustering scenario without a prior graph, these models estimate an initial graph beforehand to apply GCN.…
This paper studies the problem of counting homomorphisms from a bipartite source graph to a bipartite target graph. An exact formula is first derived for the number of homomorphisms from a complete bipartite graph into a general bipartite…
Augustine et al. [DISC 2022] initiated the study of distributed graph algorithms in the presence of Byzantine nodes in the congested clique model. In this model, there is a set $B$ of Byzantine nodes, where $|B|$ is less than a third of the…
Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called "connectomics". Connectomics studies the brain as a graph; vertices…
Co-saliency detection aims to discover the common and salient foregrounds from a group of relevant images. For this task, we present a novel adaptive graph convolutional network with attention graph clustering (GCAGC). Three major…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
Deep graph clustering (DGC), which aims to unsupervisedly separate the nodes in an attribute graph into different clusters, has seen substantial potential in various industrial scenarios like community detection and recommendation. However,…
Recent research on deep graph learning has shifted from static to dynamic graphs, motivated by the evolving behaviors observed in complex real-world systems. However, the temporal extension in dynamic graphs poses significant data…