# Research

2. For bigger image : right click, “open image in new tab”

## Work in progress

• Phase transition boundary of minimum volume matrix factorisation problem : the rank-deficient cases and the asymmetric non-separable cases
What : The theoretical paper on proving the phase transition boundary between solvable and unsolvable problems in convex hull fitting problems of volume regularised NMF under rank deficient cases and asymmetric non-separable cases (long project, work in progress)

• On Nonlinear GMRES optimization for non-negative matrix factorizations
What : N-GMRES, multi-step methods (Work in progress)

• A Fast Algorithm for Non-negative Inverse Problems
What : a paper on convergence proof, more mathematical than applied. (Work in progress)

• $$\beta$$-NMF for blind audio source separation with minimum volume regularization
What : journal version of the work on blind audio source separation via logdet-volume regularized $$\beta$$-NMF, on piano and drum set audio
(Work in progress, almost finish)

## Pre-print/ Under-review

### Séparation aveugle de sources sonores par factorization en matrices positives avec pénalité sur le volume du dictionnaire

IN FRENCH
What : blind audio source separation via logdet-volume regularized $$\beta$$-NMF
😁 : the result is very good on Bach Prelude on piano
Submitted to GRETSI2019
[Conference preprint]

### Accelerating Nonnegative Tensor Factorization Algorithms using Extrapolation

What : the tensor extension of the work J2
😁 : the result for ‘‘proof of concept“ is already crazily good (even better than existing accelerated methods)
Submitted to GRETSI2019
[Conference preprint] [MATLAB]

### Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing

What : the long version of C4, new things include assymetric non-separability and nuclear norm regularisation
Result : logdet-volume regularisation is generally better than the det-volume regularisation
😁 : the result is better than the state-of-the-art algorithm RVolMin of Fu2016
Submitted to IEEE JSTARS, under review
[Preprint] [MATLAB]

## Journal Papers

### J2.Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation

Neural Computation, vol. 31, issue 2, pp 417-439, Feburary 2019, MIT Press
(Submitted May 18, 2018; accepted September 26, 2018, online available December 21, 2018)
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 state-of-the-art algorithm Block proximal linearized method APG-MF of Xu & Yin 2013
☹ : no theoretical convergence – hard to prove, working in progress
[DOI], [arXiv], [MATLAB], [Slide], [Old slide 1], [Old slide 2, for IMSP2018]

An example by running the MATLAB code (link above) for 10 seconds.

Presented in

• OR2018, Brussels, Belgium, 2018.09.14

• ISMP 2018, Bordeaux, France, 2018.07.05

## Conference papers

### C5. Minimum-Volume Rank-deficient Non-negative Matrix Factorizations

What : volume regularised NMF also works for rank deficient case
😁 : first study on relaxing the full rank assumption of the factor matrix in minimum volume NMF
☹ : no theory yet
Accepted by IEEE ICASSP 2019
[Conference preprint][MATLAB]

### C4.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
😁 : proposed method (Eigen) is fast for this special problem compared with det regularisation and Taylor series approximation of logdet
☹ : no theoretical convergence – hard to prove, working in progress
[Short slide], [Full slide (last updated 2018-May-18)], [conference poster], [conference preprint],

Presented in

• IEEE WHISPERS 2018, Amsterdam, Netherlands, 2018.09.25

• inforTech'Day 2018, Mons, Belgium, 2018.05.16.

• SIAM ALA18, Hong Kong Baptist University, Hong Kong, 2018.05.04

• ORBEL32, University of Liège, Liège, Belgium, 2018.02.01

• XMaths Workshop, University of Bari Aldo Moro, Bari, Italy, 2017.12.20

• University of Hong Kong, Hong Kong, 2017.11.30

• Chinese University of Hong Kong, Hong Kong, 2017.11.27

## Other stuffs : presentations / posters

2017.08.28 Log-determinant constrained Non-negative Matrix Factorization
[Poster presentation in Autumn School : Optimization in Machine Learning and Data Science, in Trier University, Trier, Germany]
My second presentation, got some advices from Stephen Wright during the autumn school.

2017.05.19 A Low-rank regularized Non-negative Matrix Factorization Model
[A short presentation in front of Stephen Boyd, Yurri Nesterov and Francois Glineur in UCL, Belgium]
My first presentation after I started my PhD in Belgium since 2017-Feb. I have to admit, the meeting was super exciting.

### Old works before 2017.02

C3. 2016 Leveraging videos and forums for small-class learning experience in a MOOC environment IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE)

C2. 2016 A Non-negative Tensor Factorization Approach to Feature Extraction for Image Analysis 2016 IEEE International Conference on Digital Signal Processing (DSP)