Non-negative Matrix Factorisation with Topological Regularisation
Non-negative matrix factorisation (NMF) learns additive representations from data, but non-negativity alone does not ensure interpretable basis functions. We introduce Top-NMF, which guides basis learning through general topological preferences without prescribing the detailed form of the components. Observations and basis vectors are treated as non-negative functions on structured domains. Discrete topological conditions are difficult to optimise directly. Our guiding viewpoint is that persistent homology provides a stable, continuous relaxation of ordinary homological invariants: it tracks connected components and loops across thresholds, allowing structural preferences to be expressed ...
| Authors | Matias de Jong van Lier, Shizuo Kaji, Keunsu Kim |
|---|---|
| Primary category | cs.LG |
| Published | 16 June 2026 |
| Last updated at source | 29 September 2026 |
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