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

Vincent C.K. Cheung, Karthik Devarajan, Giacomo Severini, Andrea Turolla, Paolo Bonato

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publication2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3496-3499
Number of pages4
ISBN (Electronic)9781424492718
DOIs
StatePublished - Nov 4 2015
Event37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2015 - Milan, Italy
Duration: Aug 25 2015Aug 29 2015

Publication series

NameProceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS
Volume2015-November
ISSN (Print)1557-170X

Conference

Conference37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2015
Country/TerritoryItaly
CityMilan
Period08/25/1508/29/15

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