312. Riemannian Optimization on Nonnegative Matrix Factorizations: chordal, oblique and more
Invited abstract in session TC-11: Advances in Manifold and Conic Optimization, stream Riemannian Manifold and Conic Optimization.
Tuesday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Man Shun Andersen Ang
|
| CS, University of Southampton | |
| 2. | Flavia Esposito
|
| Department of Mathematics, University of Bari Aldo Moro |
Abstract
Nonnegative Matrix Factorization (NMF) approximates a nonnegative matrix as a conic combination of two nonnegative, low-rank matrices. We explore Riemannian optimization in NMF through two examples.
1. Chordal-NMF: We replace the "point-to-point" distance in NMF with a ray-to-ray chordal distance, casting Chordal-NMF onto a manifold. Unlike prior methods requiring smooth manifolds, nonnegativity here yields a non-differentiable one. We propose a Riemannian Multiplicative Update (RMU) that ensures convergence without smoothness, showing its efficacy on multispectral images.
2. Sparse Orthogonal NMF: We add a nonconvex ell_{0.5}-quasi-norm for sparsity and orthogonal constraints to NMF factors. Replacing nonnegativity with a Hadamard product, we solve it via RMU on the Oblique manifold.
If time permit, we’ll discuss NMF on the Stiefel manifold, SO(n), and entropic regularization in Lie groups.
Joint works with Flavia Esposito (Università degli Studi di Bari Aldo Moro).
Keywords
- First-order optimization
- Non-smooth optimization
- Optimization for learning and data analysis
Status: accepted
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