![[2602.22536] Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.22536] Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization
Summary
The paper introduces Persistent Nonnegative Matrix Factorization (pNMF), a novel approach that utilizes multi-scale graph regularization to enhance dimensionality reduction and data representation, addressing limitations of traditional NMF methods.
Why It Matters
This research is significant as it advances the field of machine learning by providing a method that captures multi-scale connectivity structures, which is crucial for applications in data analysis and interpretation, particularly in complex datasets like single-cell RNA sequencing.
Key Takeaways
- pNMF offers a sequence of persistence-aligned embeddings rather than a single output.
- The method incorporates persistent homology to identify critical scales of connectivity changes.
- A new coupled NMF formulation is introduced, enhancing cross-scale consistency.
- The proposed algorithm ensures guaranteed convergence, addressing computational challenges.
- Numerical experiments validate the effectiveness of pNMF in multi-scale low-rank embeddings.
Computer Science > Machine Learning arXiv:2602.22536 (cs) [Submitted on 26 Feb 2026] Title:Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization Authors:Jichao Zhang, Ran Miao, Limin Li View a PDF of the paper titled Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization, by Jichao Zhang and 2 other authors View PDF HTML (experimental) Abstract:Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale and fail to capture the evolution of connectivity structures across resolutions. In this work, we propose persistent nonnegative matrix factorization (pNMF), a scale-parameterized family of NMF problems, that produces a sequence of persistence-aligned embeddings rather than a single one. By leveraging persistent homology, we identify a canonical minimal sufficient scale set at which the underlying connectivity undergoes qualitative changes. These canonical scales induce a sequence of graph Laplacians, leading to a coupled NMF formulation with scale-wise geometric regularization and explicit cross-scale consistency constraint. We analyze the structural properties of the embeddings along the scale parameter and establish bounds on their increments between consecutive scales. The resulting model defines a nontrivial solution path across scales, rathe...
