The paper introduces an efficient method for learning balanced signed graph Laplacians directly from data. By extending the CLIME sparse inverse covariance estimation framework, it formulates a linear programming problem for each Laplacian column with sign constraints that enforce positive edges between nodes of the same polarity and negative edges otherwise. The authors develop a tailored ADMM-based sparse LP solver, prove convergence properties, and demonstrate through experiments that the learned balanced graphs outperform existing methods and allow the reuse of spectral filtering tools, wavelets, and graph neural networks designed for positive graphs.
By Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung
The paper investigates how signed graph filters respond to structural changes such as edge additions, deletions, and sign flips. It shows that both the nature of the edge perturbation and the correlation among node features jointly influence the stability of learned representations. Leveraging this insight, the authors propose a perturbation strategy that targets structurally influential signed edges, and experiments demonstrate that this approach causes greater embedding drift, polarity change, and link‑prediction degradation than baseline methods.
By Ning Zhang, Li Zhang
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
By Adam M. Oberman
arXiv:2609.23668v1 Announce Type: cross
Abstract: Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constra...
By Christoffer Kjellson, Claudio Altafini, Emma Tegling
The paper investigates how to recover low‑dimensional latent geometry from a random geometric graph built from noisy, high‑dimensional data. It analyzes a spectral embedding algorithm on the Signal+Noise Graph Model, where vertices are perturbed points and edges are added when their inner product exceeds a threshold. In the regime where both the number of points and ambient dimension grow, the authors prove that, under a spectral gap condition, the leading eigenvectors and eigenvalues of the adjacency matrix can approximately recover the original point cloud up to an orthogonal transformation, and demonstrate the method on nested spheres and high‑dimensional sinusoid curves.
By Tatiana Brailovskaya, Nicholas A. Cook, Sofia Poinelli
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
By Charles Dufour, Ulysse Naepels, Leonardo V. Santoro
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
By Ecem Bozkurt, Antonio Ortega
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
By Rajath Rao K. N., Jens Schl\"oter, Sami Davies, Amira Ouchene, Yasamin Nazari
The paper introduces LENS, a lightweight algorithm that detects noisy labels in graph data by measuring how removing a node reduces neighborhood entropy. It shows that label noise increases entropy and blurs class boundaries, and proposes a relabeling step to preserve useful features. Experiments demonstrate that LENS outperforms existing noise‑robust methods in accuracy while being an order of magnitude faster.
By Pintu Kumar, Nandyala Hemachandra
arXiv:2608. 00836v1 Announce Type: new Abstract: While signed-directed graphs have been studied using linear Laplacians in the design of graph neural networks, relatively little research has focused on developing non-linear Laplacian operators for such networks.
By Ali Parviz, Yuichi Yoshida
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 L...
By Jinchuan Liao, Dai Hai Nguyen
arXiv:2607. 03587v1 Announce Type: new Abstract: We propose NetinfoGC, a framework for graph classification that extends the Network Usable Information (NUI) paradigm to graph-level learning.
By Abdullah Shaik, Anwar Said