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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Decomposing time series data by a non-negative matrix factorization algorithm with temporally constrained

Vincent C K Cheung, Karthik Devarajan, Giacomo Severini

    Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
    |January 7, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a modified non-negative matrix factorization (NMF) algorithm to better analyze time series data by incorporating temporal dependencies. The enhanced NMF method objectively identifies muscle synergies in human upper-limb movement data.

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    Area of Science:

    • Biomedical Engineering
    • Computational Neuroscience
    • Robotics

    Background:

    • Standard non-negative matrix factorization (NMF) assumes data independence, limiting its application to time series data with temporal correlations.
    • Analyzing complex biological signals like electromyography (EMG) requires methods that account for the sequential nature of data.
    • Identifying muscle synergies in human movement is crucial for understanding motor control and developing assistive technologies.

    Purpose of the Study:

    • To develop a modified NMF algorithm that incorporates temporal dependencies for improved time series data analysis.
    • To apply the modified NMF to electromyographic (EMG) data for objective identification of muscle synergies.
    • To compare the model order determined by the modified NMF with traditional ad hoc methods.

    Main Methods:

    • A novel NMF algorithm was derived by incorporating a simple temporal constraint into the coefficient update rules.
    • The modified NMF algorithm was applied to two multi-dimensional EMG datasets from the human upper limb.
    • The Akaike Information Criterion (AIC) was used to objectively determine the model order (number of muscle synergies).

    Main Results:

    • The modified NMF successfully accounted for temporal dependencies in the EMG data.
    • The algorithm reduced the number of free parameters, enabling objective model order selection using AIC.
    • The identified muscle synergies were functionally interpretable and consistent with previously reported findings.

    Conclusions:

    • The modified NMF algorithm provides a robust framework for analyzing time series data with temporal correlations.
    • This approach offers an objective method for determining the number of muscle synergies, improving upon ad hoc measures.
    • The findings have implications for motor control research, biomechanics, and the development of neuroprosthetics.