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
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: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
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
arXiv:2502.04312v3 Announce Type: replace
Abstract: Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its...
By Chenghui Li, A. Martina Neuman
arXiv:2605. 22346v2 Announce Type: replace-cross Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same graph.
By Minh Triet Pham, Ian Gallagher
arXiv:2607. 21263v1 Announce Type: new Abstract: Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice.
By Purui Zhang, Feng Ji, Yanan Zhao, Bihan Wen, Wee Peng Tay
arXiv:2608. 10845v1 Announce Type: cross Abstract: Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian.
By John Park, Ning Hao