Title: Nonnegative Matrix Factorization in non-standard settings, for fun
| Speaker: | Andersen Ang |
| Affiliation: | University of Southampton |
| Location: | MC 6029 |
Abstract: This abstract is broken into 6 points.
1. What is NMF: NMF is to find two elementwise nonnegative low-rank matrices W and H such that M ≈ WH for a given elementwise nonnegative matrix M.
2. NMF is commonly done in the Euclidean distance.
3. I argue that Euclidean distance is "not good", and a ray-to-ray distance is better.
4. Under L2-normalization onto the unit sphere, we arrive at the cosine angle distance, which motivates the use of manifold optimization techniques.
5. Under L1-normalization onto the simplex, we arrive at the so-called Aitchison geometry, which contains funny algebra.
6. Why do these: for curiosity and fun. For application, these non-standard NMF can "remove cloud" from satellite images.