arXiv AI By Jinghui Yuan, Chusheng Zeng, Fangyuan Xie, Zhe Cao, Mulin Chen, Rong Wang, Feiping Nie, Yuan Yuan

Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping

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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.

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arXiv Machine Learning
Aug 31

Optimal Transport for Network Comparison: A Review with Machine Learning Applications

The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.

By James Hyun, Fran\c{c}ois G. Meyer