Decomposing time series data by a non-negative matrix factorization algorithm with temporally constrained coefficients

The non-negative matrix factorization algorithm (NMF) decomposes a data matrix into a set of non-negative basis vectors, each scaled by a coefficient. In its original formulation, the NMF assumes the data samples and dimensions to be independently distributed, making it a less-than-ideal algorithm f...

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Bibliographic Details
Published in:2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) Vol. 2015; pp. 3496 - 3499
Main Authors: Cheung, Vincent C. K., Devarajan, Karthik, Severini, Giacomo, Turolla, Andrea, Bonato, Paolo
Format: Conference Proceeding Journal Article
Language:English
Published: United States IEEE 01.08.2015
Subjects:
Algorithms
Data mining
Data models
Distributed databases
Electromyography
Humans
Matrix decomposition
Models, Theoretical
Muscles
Muscles - physiology
Time Factors
Time series analysis
ISSN:1094-687X, 1557-170X, 2694-0604, 2694-0604
Online Access:Get full text
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Summary:The non-negative matrix factorization algorithm (NMF) decomposes a data matrix into a set of non-negative basis vectors, each scaled by a coefficient. In its original formulation, the NMF assumes the data samples and dimensions to be independently distributed, making it a less-than-ideal algorithm for the analysis of time series data with temporal correlations. Here, we seek to derive an NMF that accounts for temporal dependencies in the data by explicitly incorporating a very simple temporal constraint for the coefficients into the NMF update rules. We applied the modified algorithm to 2 multi-dimensional electromyographic data sets collected from the human upper-limb to identify muscle synergies. We found that because it reduced the number of free parameters in the model, our modified NMF made it possible to use the Akaike Information Criterion to objectively identify a model order (i.e., the number of muscle synergies composing the data) that is more functionally interpretable, and closer to the numbers previously determined using ad hoc measures.
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ISSN:1094-687X
1557-170X
2694-0604
2694-0604
DOI:10.1109/EMBC.2015.7319146