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The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We introduce the concept of a $k$-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the…
This paper proposes a parameter collaborative optimization algorithm for large language models, enhanced with graph spectral analysis. The goal is to improve both fine-tuning efficiency and structural awareness during training. In the…
Consider a random graph $G$ of size $N$ constructed according to a \textit{graphon} $w \, : \, [0,1]^{2} \mapsto [0,1]$ as follows. First embed $N$ vertices $V = \{v_1, v_2, \ldots, v_N\}$ into the interval $[0,1]$, then for each $i < j$…
Graph matching aims to find correspondences between two graphs. It is a fundamental task in pattern recognition. The classical spectral matching algorithm has time complexity $\mathcal{O}(n^4)$ and space complexity $\mathcal{O}(n^4)$, where…
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…
Laplacian spectral kernels and distances (e.g., biharmonic, heat diffusion, wave kernel distances) are easily defined through a filtering of the Laplacian eigenpairs. They play a central role in several applications, such as dimensionality…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
We consider a model of stable edge sets (``matchings'') in a bipartite graph $G=(V,E)$ in which the preferences for vertices of one side (``firms'') are given via choice functions subject to standard axioms of consistency, substitutability…
Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Graph signal processing (GSP) deals with the representation, analysis, and processing of structured data, i.e. graph signals that are defined on the vertex set of a generic graph. A crucial prerequisite for applying various GSP and graph…
In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition…
This paper considers the problem of estimating high dimensional Laplacian constrained precision matrices by minimizing Stein's loss. We obtain a necessary and sufficient condition for existence of this estimator, that consists on checking…
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…