Elsevier

Biosystems

Volume 82, Issue 3, December 2005, Pages 273-284
Biosystems

Generative topographic mapping applied to clustering and visualization of motor unit action potentials

https://doi.org/10.1016/j.biosystems.2005.09.004Get rights and content

Abstract

The identification and visualization of clusters formed by motor unit action potentials (MUAPs) is an essential step in investigations seeking to explain the control of the neuromuscular system. This work introduces the generative topographic mapping (GTM), a novel machine learning tool, for clustering of MUAPs, and also it extends the GTM technique to provide a way of visualizing MUAPs. The performance of GTM was compared to that of three other clustering methods: the self-organizing map (SOM), a Gaussian mixture model (GMM), and the neural-gas network (NGN). The results, based on the study of experimental MUAPs, showed that the rate of success of both GTM and SOM outperformed that of GMM and NGN, and also that GTM may in practice be used as a principled alternative to the SOM in the study of MUAPs. A visualization tool, which we called GTM grid, was devised for visualization of MUAPs lying in a high-dimensional space. The visualization provided by the GTM grid was compared to that obtained from principal component analysis (PCA).

Introduction

The clustering of motor unit action potentials (MUAPs) is an important stage in the analysis of the behavior of the neuromuscular system. This analysis can reveal how many motor units are active during a muscle contraction, and also identify the waveform that best represents the MUAPs of a particular motor unit, which is often referred to as the MUAP template.

Over the last 20 years numerous strategies for estimating MUAP templates and identification of the number of active motor units have appeared LeFever and De Luca, 1982, Mambrito and De Luca, 1984, McGill et al., 1985, Joynt et al., 1991, Stashuk and Naphan, 1992, Hassoun et al., 1994, Etawil and Stashuk, 1996, Stashuk and Paoli, 1998, Christodoulou and Pattichis, 1999, Stashuk, 2001, Zennaro et al., 2003. Most of them have the clustering stage as part of a more complex system formed by other signal processing steps, such as, signal filtering, detection, feature extraction or selection, and data classification.

Despite the large number of tools available for investigation or extraction of MUAPs from electromyographic signals, there exists a lack of tools that allow for a simultaneous visualization and clustering of MUAP data sets. Such tools may be relevant for an exploratory analysis of the data. In contrast to a fully automatic system, this exploratory investigation allows the user or specialist to identify relevant features in the data.

Visualization and clustering of MUAPs together may allow the experimenter to identify relevant patterns in electromyographic signals. Such patterns (MUAPs) are generated from the neuromuscular system and therefore they reflect the internal state of such a system, as recorded potentials result from ionic currents, which are generated from the movement of sodium and potassium ions in muscle fibres. From the analysis of the shape of these MUAPs it is possible, for example, to make enquiries about the state of muscle and nerves, which makes a simultaneous visualization and clustering of MUAPs an additional and relevant tool for practical investigations regarding detection of neuromuscular disorders.

Additionally, in practice, MUAPs obtained from experimental EMG signals lie in a high-dimensional space and are not grouped into logical units (clusters), which makes it difficult for the experimenter/researcher or clinician to discriminate them. In this context, tools which allow the simultaneous visualization and clustering of MUAPs play an important role. First, they group similar MUAPs into clusters and secondly they provide the investigator with visual information about distances between MUAP clusters lying in a lower-dimensional space. These distances represent differences among MUAP shapes which in a lower-dimensional space may be easily perceived and thus analyzed by the investigator.

This technique may also be employed for monitoring and feedback. For instance, Basmajian and Luca (1985) pointed out that the visualization of MUAPs may be used as a biofeedback tool, where patients or subjects could control muscle strength based on the system output (visualization of MUAPs) in psychological and rehabilitative treatments.

The work presented in this paper is focused on the clustering and visualization of motor unit action potentials. In particular, the generative topographic mapping (GTM) Svensen, 1998, Bishop et al., 1998, Bishop and Svensen, 1998, a novel machine learning tool for data modeling and visualization, is employed for the analysis of electromyographic signals.

The GTM was designed to be a principled alternative tool to the self-organizing map (SOM). The main motivation for the development of GTM was to devise a tool that solves some of the theoretical problems related to SOM. Two of these are highlighted below:

  • So far, rigorous convergence proofs for the learning of a feature map have only been obtained for the 1D case (Ritter, 2001).

  • The SOM training algorithm does not optimize an objective function (Svensen, 1998).

Despite such theoretical flaws the SOM has been successfully applied to solve many practical problems since its inception. Furthermore, the implementation of the SOM algorithm is much less complex than the GTM algorithm. Thus, an important issue was to compare the performance of these methods in practice by using the same experimental data. One of the aims of this paper is to present the results of this comparison based on the analysis of electromyographic signals, or the clustering of motor unit action potentials. Such a study had not been performed before.

The discussion in the following sections presents a review of the clustering techniques employed in this work, and the results of the comparison of the performance of GTM to that of three other clustering methods: a Gaussian mixture model (GMM), the SOM and the neural-gas network (NGN). In addition, we show how GTM may be employed as a tool that provides simultaneous visualization and clustering of MUAPs lying in a high-dimensional space. This novel visualization strategy, the so-called GTM grid, is compared to that obtained from principal component analysis (PCA).

Section snippets

A brief review of clustering techniques

This section describes the techniques for data clustering or analysis employed in this work.

Data collection

Ethical approval for this research was granted by the Ethical Committee of the National Health Service of the United Kingdom (Berkshire Local Research Ethics Committee—reference number 33/04) and by the Ethical Committee of the University of Reading. A consent form was signed by each subject before data collection.

Electromyographic signals were collected from the first dorsal interosseous (one of the muscles of hand) of 10 subjects. The signal was differentially amplified via a commercial

Evaluation of performance of clustering techniques

Prior to the clustering of the data sets shown in Fig. 5, Fig. 6, Fig. 7, patterns were randomly shuffled in order to avoid any potential bias.

Two different protocols were adopted for data clustering. In the first, all data were used for training and evaluation of GTM, GMM, SOM and NGN. In the second, the data were randomly divided into two approximately equal parts and one was used for training and the other for assessment. Since these clustering techniques may be sensitive to random

Performance of clustering techniques

This work has introduced the application of the generative topographic mapping (GTM) to the clustering and visualization of motor unit action potentials. Since GTM is a relatively recent technique it was important to compare its performance to that of some related methods. The results presented in Table 1, Table 2 indicate that the performances of GTM and SOM were superior to those of GMM and NGN. They also showed that the rates of success of GTM and SOM were very similar with a difference of

Acknowledgment

The authors would like to thank the Brazilian government (CNPq) for the financial support of this research.

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