Related papers: Topologically Attributed Graphs for Shape Discrimi…
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
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…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Representation learning has overcome the often arduous and manual featurization of networks through (unsupervised) feature learning as it results in embeddings that can apply to a variety of downstream learning tasks. The focus of…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…
A Reeb graph is a graphical representation of a scalar function on a topological space that encodes the topology of the level sets. A Reeb space is a generalization of the Reeb graph to a multiparameter function. In this paper, we propose…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
Graph classification is a significant problem in many scientific domains. It addresses tasks such as the classification of proteins and chemical compounds into categories according to their functions, or chemical and structural properties.…
We present attributed hierarchical port graphs (AHP) as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems. AHP consist of a number of interconnected layers, where each layer…
Graph structured data provide two-fold information: graph structures and node attributes. Numerous graph-based algorithms rely on both information to achieve success in supervised tasks, such as node classification and link prediction.…
Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This…