This document discusses non-negative matrix factorization (NMF) and its application to electromyography (EMG) sampled signals. NMF decomposes a non-negative data matrix into two non-negative matrices, approximating the original matrix. It has been used to extract muscle synergies from EMG data, with the data matrix representing EMG signals and the output matrices representing muscle synergies and their activations over time. The document also briefly compares FPGAs, microprocessors and microcontrollers for implementing NMF in real-time on hardware, noting that FPGAs allow real-time NMF with acceptable energy costs.

1. 1
Rolando Brondolin rolando.brondolin@mail.polimi.it
LucaCerina luca.cerina@mail.polimi.it
AlessandraFusco alessandra1.fusco@mail.polimi.it

2. SynCH Design
2Images from https://backyardbrains.com/ and http://techmog.com

3. Focus on NMF (1)
3
Non-negative Matrix Factorization (NMF)

4. 4
Focus on NMF (2)
Given a nonnegative matrix A Rm×n and a positive integer k < min{m, n} find
nonnegative matrices W Rm×k and H Rk×n to minimize the functional:
Img: Cheung, Vincent CK, et al. "Muscle synergy patterns as physiological markers of motor cortical damage." Proceedings of the National Academy of Sciences 109.36 (2012): 14652-14656.
A -> EMG sampled signal, W -> Muscle Synergy, H -> Time-varying activation

5. 5
NMF heuristics iteratively updates W and H and converges to a local optimal solution,
checking at each step the value of the cost function. Polynomial time[1], but still
expensive!
[1] Vavasis, Stephen A. "On the complexity of nonnegative matrix factorization." SIAM Journal on Optimization 20.3 (2009): 1364-1377.
FPGAs
• High power
• Low energy consumption
• Difficult to develop
• Real-time NMF feasible with
acceptable energy costs
Microprocessors
• High power
• High Energy consumption
• Real-time NMF feasible but at
high energy cost
Microcontrollers
• Low power
• Low Energy
• Real-time NMF not feasible on
site, external CPU is needed
Chosen architecture

6. Rolando Brondolin rolando.brondolin@mail.polimi.it
LucaCerina luca.cerina@mail.polimi.it
AlessandraFusco alessandra1.fusco@mail.polimi.it
Synch - Synergically controlled hand
(www.facebook.com/synchnecst)
@SynCHNecst
(www.twitter.com/SynCHNecst)