aiqbench analysis
This research introduces a novel graph dictionary learning framework that represents graphs as Gaussian distributions derived from filtered Laplacians, optimizing reconstruction via a new surrogate distance metric. By minimizing this metric through backpropagation, the method effectively clusters and classifies graphs without requiring known node correspondences, demonstrating competitive performance on standard benchmarks. The work advances machine learning techniques for handling unaligned graph structures using optimal transport principles.
A dictionary learning framework for graphs via filters and optimal transport
arXiv:2609.05919v1 Announce Type: new Abstract: We propose a graph dictionary learning (GDL) framework where each graph is represented as a zero-mean Gaussian distribution derived from its filtered Laplacian. Each observed graph is approximated by a barycenter over learned atom graphs, computed under the filter graph distance (fGOT), a graph comparison metric sensitive to global structural properties. The reconstruction error between the observed graph and its barycenter is measured by the surrogate fGOT (sfGOT) distance, a tractable approximation of fGOT that handles graphs without known node correspondence, and is minimized end-to-end via backpropagation. We further provide a novel interpretation of sfGOT through the lens of the Hilbert-Schmidt Independence Criterion, showing that minimizing the sfGOT distance between two graphs is equivalent to maximizing statistical dependence between the spectral embedding of their nodes. Experiments on benchmark datasets demonstrate competitive performance over existing GDL methods on graph clustering and classification tasks.
Abstract:We propose a graph dictionary learning (GDL) framework where each graph is represented as a zero-mean Gaussian distribution derived from its filtered Laplacian. Each observed graph is approximated by a barycenter over learned atom graphs, computed under the filter graph distance (fGOT), a graph comparison metric sensitive to global structural properties. The reconstruction error between the observed graph and its barycenter is measured by the surrogate fGOT (sfGOT) distance, a tractable approximation of fGOT that handles graphs without known node correspondence, and is minimized end-to-end via backpropagation. We further provide a novel interpretation of sfGOT through the lens of the Hilbert-Schmidt Independence Criterion, showing that minimizing the sfGOT distance between two graphs is equivalent to maximizing statistical dependence between the spectral embedding of their nodes. Experiments on benchmark datasets demonstrate competitive performance over existing GDL methods on graph clustering and classification tasks.
Machine Learning (cs.LG)
arXiv:2609.05919 [cs.LG]
(or arXiv:2609.05919v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.05919 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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