Related papers: Consistent Manifold Representation for Topological…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…
Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep…
Graph-based data present unique challenges and opportunities for machine learning. Graph Neural Networks (GNNs), and especially those algorithms that capture graph topology through message passing for neighborhood aggregation, have been a…
We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…
We propose a novel approach for visual representation learning called Signature-Graph Neural Networks (SGN). SGN learns latent global structures that augment the feature representation of Convolutional Neural Networks (CNN). SGN constructs…
Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation…
Motivated by the enumeration of the BPS spectra of certain 3d $\mathcal{N}=2$ supersymmetric quantum field theories, obtained from the compactification of 6d superconformal field theories on three-manifolds, we study the homeomorphism…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and…
This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…
Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…
$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially…
Nearest neighbor (k-NN) graphs are widely used in machine learning and data mining applications, and our aim is to better understand what they reveal about the cluster structure of the unknown underlying distribution of points. Moreover, is…
Graph representation learning is a fundamental task in various applications that strives to learn low-dimensional embeddings for nodes that can preserve graph topology information. However, many existing methods focus on static graphs while…
The complicated syntax structure of natural language is hard to be explicitly modeled by sequence-based models. Graph is a natural structure to describe the complicated relation between tokens. The recent advance in Graph Neural Networks…
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional…
We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…
Graph neural networks (GNNs) on text--attributed graphs (TAGs) typically encode node texts using pretrained language models (PLMs) and propagate these embeddings through linear neighborhood aggregation. However, the representation spaces of…
Graph data often contain noisy and spurious correlations that mask the true causal relationships, which are essential for enabling graph models to make predictions based on the underlying causal structure of the data. Dependence on spurious…