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What is a mathematically rigorous way to describe the taxi-pickup distribution in Manhattan, or the profile information in online social networks? A deep understanding of representing those data not only provides insights to the data…
In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Text-conditioned image generation has made significant progress in recent years with generative adversarial networks and more recently, diffusion models. While diffusion models conditioned on text prompts have produced impressive and…
Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…
Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
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…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
In this work, we introduce a new algorithm for analyzing a diagram, which contains visual and textual information in an abstract and integrated way. Whereas diagrams contain richer information compared with individual image-based or…
Graph neural networks (GNNs) encounter significant computational challenges when handling large-scale graphs, which severely restricts their efficacy across diverse applications. To address this limitation, graph condensation has emerged as…
Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediate benefits for various graph learning tasks. However, existing graph condensation methods rely…
The recent past has seen an increasing interest in Heterogeneous Graph Neural Networks (HGNNs), since many real-world graphs are heterogeneous in nature, from citation graphs to email graphs. However, existing methods ignore a tree…
This study presents a hierarchical mining framework for high-dimensional imbalanced data, leveraging a depth graph model to address the inherent performance limitations of conventional approaches in handling complex, high-dimensional data…
Many data science applications like social network analysis use graphs as their primary form of data. However, acquiring graph-structured data from social media presents some interesting challenges. The first challenge is the high data…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…