The paper introduces a degree‑corrected joint matrix factorization technique for detecting communities in multilayer networks. It uses a nonnegative symmetric matrix trifactorization that enforces disjoint, shared communities across layers while allowing each layer to have distinct connectivity patterns and node degrees. An efficient algorithm is presented and evaluated on a multilayer degree‑corrected stochastic block model, showing superior performance compared to existing methods.
By Alexandra Dache, Manon Rustin, Arnaud Vandaele, Nicolas Gillis
The paper introduces the Marcus mapping, an extension of Marcus theorem that allows certain sparse symmetric matrices to be transformed into doubly stochastic symmetric matrices via diagonal matrices. Leveraging this mapping, the authors propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm (ANCMM), which incorporates rank constraints to ensure the learned similarity graph naturally partitions into the desired number of clusters. Experiments demonstrate ANCMM’s effectiveness compared to state‑of‑the‑art methods, and the authors also establish a connection between the Marcus mapping and a specific optimal transport problem.
By Jinghui Yuan, Chusheng Zeng, Fangyuan Xie, Zhe Cao, Mulin Chen, Rong Wang, Feiping Nie, Yuan Yuan
arXiv:2608.21607v1 Announce Type: cross
Abstract: We investigate when a sparse nonnegative matrix can be recovered from a real-valued matrix of much lower rank by zeroing out its negative elements. T...
By Lawrence K. Saul, Ningyuan Huang, Dennis Bollweg, Jeff Soules, Diana C. Halikias
arXiv:2608.29362v1 Announce Type: cross
Abstract: Sparse computations are fundamental to scientific computing, graph analytics, and machine learning, yet their performance is highly sensitive to the...
By Ruifeng Zhang, Xipeng Shen
arXiv:2607. 24338v1 Announce Type: new Abstract: Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data.
By Zengyi Wo, Shiyu Zhang, Qiyao Peng, Tianpeng Li, Xuan Guo
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
By Zhuan Liang, Zheng Zhai
The paper introduces an unsupervised framework that merges manifold learning with rank‑based interpretable graph embeddings to address the Geometric and Interpretability Gaps in visual representation learning. By first analyzing contextual information on the dataset manifold and then producing sparse, self‑explainable embeddings, the method achieves dimensionality reduction while preserving or improving performance in image retrieval and semi‑supervised Graph Convolutional Network classification. Experiments across varied datasets confirm that these context‑aware representations maintain high downstream effectiveness.
By Thiago C\'esar Castilho Almeida, Gustavo Rosseto Let\'icio, Vinicius Atsushi Sato Kawai, Daniel Carlos Guimar\~aes Pedronette
The paper introduces Spectral Connectivity-Regularized Graph Learning (SCoGL), a method for learning sparse graphs from limited data by incorporating Laplacian spectral priors that promote global connectivity. SCoGL extends the graphical lasso objective with a connectivity prior derived from Laplacian eigenvalues and uses projected gradient descent with Armijo backtracking for optimization. Experiments demonstrate that SCoGL improves graph recovery and enhances downstream tasks such as graph signal denoising when observations are scarce.
By Mingxiao Liu (Tsinghua University, China), Bahar Oveisgharan (York University, Canada), Bingyan Zou (Tsinghua University, China), Gene Cheung (York University, Canada), H. Vicky Zhao (Tsinghua University, China), Feifei Gao (Tsinghua University, China)
The paper introduces a compositional graph embedding framework based on Aitchison geometry, where nodes are represented as simplex-valued mixtures over latent archetypal factors. By embedding these mixtures using isometric log-ratio coordinates, the method preserves Aitchison distances while allowing unconstrained optimization in Euclidean space, yielding intrinsically interpretable embeddings. The approach achieves competitive performance on node classification and link prediction tasks and enables principled component restriction through subcompositional coherence, allowing analysis of how archetype groups influence representations and predictions.
By Nikolaos Nakis, Chrysoula Kosma, Panagiotis Promponas, Michail Chatzianastasis, Giannis Nikolentzos
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:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
By Dai Hai Nguyen, Koji Tsuda
arXiv:2609.12445v1 Announce Type: cross
Abstract: Community detection in bipartite networks is a fundamental problem in modern data analysis, with applications in recommendation systems, biological n...
By Huan Qing