# What I do / focus / read : generally everything related to NMF

• Matrix/Tensor Factorizations

• low complexity (low-rank) model : make the problem simple

• complexity estimation : how to find the factorization rank?

• regularisation and constraints : make the problem less underdetermined/ill-pose

• Iterative non-linear programming in continuous optimisations : they are cool !

• First order methods and accelerated first order methods, with rate of convergence

• Global optimization on Non-convex optimisation

• When will a non-convex factorisation problem not so scary ?

• Convergence to global solution for a non-convex optimisation problem

• Robustness analysis of algorithm : like those what my boss did

• How large can noise be added to a noiseless structure such that the problem is still solvable?

• Finding the phase transition boundary of the factorisation model

• 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, randomised-column-subset-selection-things, randomised-algorithm-without-variance-or-convergence-proof

# Not yet published work

Valentin Leplat, Andersen M.S. Ang, Nicolas Gillis, Minimum-Volume Rank-deficient Non-negative 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 Non-negative Matrix Factorisations, IEEE WHISPERS 2018, Amsterdam, Netherlands, 2018.09.25
What : an iteratively reweighed least square formulation for minimising log-determinant 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 2018-May-18)], [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

• Work before 2017.02 (J1 and C1-2)
See “Old things”.
In short : applied researches that focus on biomedical signal processing systems, no theory/proof.