Related papers: Unified Fourier transform on graphs sampled from s…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are…
The analysis of the brain surface modeled as a graph mesh is a challenging task. Conventional deep learning approaches often rely on data lying in the Euclidean space. As an extension to irregular graphs, convolution operations are defined…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
We propose a framework that automatically transforms non-scalable GNNs into precomputation-based GNNs which are efficient and scalable for large-scale graphs. The advantages of our framework are two-fold; 1) it transforms various…
Recent studies have highlighted significant fairness issues in Graph Transformer (GT) models, particularly against subgroups defined by sensitive features. Additionally, GTs are computationally intensive and memory-demanding, limiting their…
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal…
Consider observations $y_1,\dots,y_n$ on nodes of a connected graph, where the $y_i$ independently come from $N(\theta_i, \sigma^2)$ distributions and an unknown partition divides the $n$ observations into blocks. One well-studied class of…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Transformers have become widely used in various tasks, such as natural language processing and machine vision. This paper proposes Gransformer, an algorithm based on Transformer for generating graphs. We modify the Transformer encoder to…
Multi-dimensional Fourier transforms are key mathematical building blocks that appear in a wide range of applications from materials science, physics, chemistry and even machine learning. Over the past years, a multitude of software…
Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(\vartheta,\varphi)$, $|m| \leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre…
Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…
We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
Community detection is a fundamental task in graph analysis, with methods often relying on fitting models like the Stochastic Block Model (SBM) to observed networks. While many algorithms can accurately estimate SBM parameters when the…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational…
Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph…
Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…
In the past few decades, quantum algorithms have become a popular research area of both mathematicians and engineers. Among them, uniform mixing provides a uniform probability distribution of quantum information over time which attracts a…