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.
arXiv:2609.18527v1 Announce Type: new Abstract: Structured prediction is the simultaneous prediction of multiple labels, and is widely used in various fields, such as natural language processing and...
arXiv:2608. 12757v1 Announce Type: cross Abstract: Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse.
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.
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.
arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.
arXiv:2605. 26854v2 Announce Type: replace Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis.
arXiv:2606. 02887v1 Announce Type: new Abstract: Symmetric nonnegative matrix factorization (Symmetric NMF) approximates a matrix as $WW^T$ with nonnegative rectangular factor $W$.
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs.
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.
GraphIFE addresses the class imbalance problem in graph-structured data by tackling a quality inconsistency issue in synthesized nodes. The framework uses graph invariant learning to strengthen embedding space representations and identify invariant features, leading to improved performance on minority classes. Experiments show that GraphIFE consistently outperforms various baselines across multiple datasets.
arXiv:2209. 00546v5 Announce Type: replace-cross Abstract: Signed and directed networks are ubiquitous in real-world applications.
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations.