What I do / focus / read : generally everything related to NMF
Matrix/Tensor Factorizations
low complexity (lowrank) model : make the problem simple
complexity estimation : how to find the factorization rank?
regularisation and constraints : make the problem less underdetermined/illpose
Iterative nonlinear programming in continuous optimisations : they are cool !
Global optimization on Nonconvex optimisation
Robustness analysis of algorithm : like those what my boss did
Other things that are interesting
Analytic continuation : for parameter tuning in regularized problems
Random matrix theory : so you still using the elbow of the scree plot of PCA?
lifting technique : problem is hard in original form? Lift it to a bigger space so that the problem is easier (but more expensive) to solve !
Discrete optimisation, extended formulation, polytope geometry
Computational complexity theory
What I don't read : “deep” things, randomisedcolumnsubsetselectionthings, randomisedalgorithmwithoutvarianceorconvergenceproof
Not yet published work
Valentin Leplat, Andersen M.S. Ang, Nicolas Gillis, MinimumVolume Rankdeficient Nonnegative Matrix Factorizations
What : volume regularised NMF also works for rank deficient case
[conference preprint]
Journal Papers
J2. Andersen Man Shun Ang, Nicolas Gillis, Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation, to appear in Neural Computation
What : solving NMF using extrapolation – update \(W^* = W_n + \beta(W_n  W)\) where \(W_n\) and \(W\) are the previous two iterates and parameter \(\beta \in [0,1]\) (similarly for \(H\)).
😁 : simple, deterministic approach, in “line search” style, very fast – faster than the Block proximal linearized method of (Xu & Yin 2013)
☹ : no theoretical convergence – hard to prove, working in progress
[arXiv], [MATLAB], [Slide], [Old slide 1], [Old slide 2, for IMSP2018]
Presented in
OR2018, Brussels, Belgium, 2018.09.14
ISMP 2018, Bordeaux, France, 2018.07.05
Conference papers
C3. Andersen Man Shun Ang, Nicolas Gillis, Volume regularized Nonnegative Matrix Factorisations, IEEE WHISPERS 2018, Amsterdam, Netherlands, 2018.09.25
What : an iteratively reweighed least square formulation for minimising logdeterminant regularized NMF
Finding : in fact no need to do complicated det regularisation nor Taylor series approximation of logdet, a simple column \(l_2\) regularisation is enough
😁 : proposed method is fast for this special problem
☹ : no theoretical convergence – hard to prove, working in progress
[Short slide],
[Full slide (last updated 2018May18)],
[conference poster],
[conference preprint],
[Full paper (later, still can be improved)]
Presented in
Chinese University of Hong Kong, Hong Kong, 2017.12.27
University of Hong Kong, Hong Kong, 2017.11.30
XMaths Workshop, University of Bari Aldo Moro, Bari, Italy, 2017.12.20
ORBEL32, University of Liège, Liège, Belgium, 2018.02.01
SIAM ALA18, Hong Kong Baptist University, Hong Kong, 2018.05.04
inforTech'Day 2018, Mons, Belgium, 2018.05.16.
IEEE WHISPERS 2018, Amsterdam, Netherlands, 2018.09.25
Other stuff : presentations / posters / old works
