The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering

2006 ◽  
Author(s):  
Tao Li ◽  
Chris Ding
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Factorization Methods

scholarly journals On identifying kinematic and muscle synergies: a comparison of matrix factorization methods using experimental data from the healthy population

2017 ◽  
Vol 117 (1) ◽  
pp. 290-302 ◽  
Author(s):  
Navid Lambert-Shirzad ◽  
H. F. Machiel Van der Loos
Keyword(s):  
Principal Component Analysis ◽  
Matrix Factorization ◽  
Muscle Activation ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Data Sets ◽  
Motor Synergies ◽  
Factorization Methods

Human motor behavior is highly goal directed, requiring the central nervous system to coordinate different aspects of motion generation to achieve the motion goals. The concept of motor synergies provides an approach to quantify the covariation of joint motions and of muscle activations, i.e., elemental variables, during a task. To analyze goal-directed movements, factorization methods can be used to reduce the high dimensionality of these variables while accounting for much of the variance in large data sets. Three factorization methods considered in this paper are principal component analysis (PCA), nonnegative matrix factorization (NNMF), and independent component analysis (ICA). Bilateral human reaching data sets are used to compare the methods, and advantages of each are presented and discussed. PCA and NNMF had a comparable performance on both EMG and joint motion data and both outperformed ICA. However, NNMF's nonnegativity condition for activation of basis vectors is a useful attribute in identifying physiologically meaningful synergies, making it a more appealing method for future studies. A simulated data set is introduced to clarify the approaches and interpretation of the synergy structures returned by the three factorization methods.NEW & NOTEWORTHY Literature on comparing factorization methods in identifying motor synergies using numerically generated, simulation, and muscle activation data from animal studies already exists. We present an empirical evaluation of the performance of three of these methods on muscle activation and joint angles data from human reaching motion: principal component analysis, nonnegative matrix factorization, and independent component analysis. Using numerical simulation, we also studied the meaning and differences in the synergy structures returned by each method. The results can be used to unify approaches in identifying and interpreting motor synergies.

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