Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping
Read the original on arXiv AI →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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