Related papers: Learning Laplacian Forms for Graph Signal Processi…
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets,…
Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective…
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised…
Graph Neural Networks (GNNs) training often necessitates gathering raw user data on a central server, which raises significant privacy concerns. Federated learning emerges as a solution, enabling collaborative model training without users…
As a bridge connecting the matching polynomial and the Laplacian matching polynomial of graphs, the subdivision method is expected to be useful for investigating the Laplacian matching polynomial. In this paper, we study applications of the…
Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…
Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…
This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph…
Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs…
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian…
To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…
HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the…
Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the…
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…
This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Graph Semi-Supervised learning is an important data analysis tool, where given a graph and a set of labeled nodes, the aim is to infer the labels to the remaining unlabeled nodes. In this paper, we start by considering an optimization-based…
Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…