IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 56, NO. 8, AUGUST 2008 4069
A Hidden Markov, Multivariate Autoregressive
(HMM-mAR) Network Framework for Analysis
of Surface EMG (sEMG) Data
Joyce Chiang, Z. Jane Wang, Member, IEEE, and Martin J. McKeown
Abstract—As the primary noninvasive means to assess muscle
activation, the surface electromyogram (sEMG) is of central
importance for the study of motor behavior in both clinical and
biomedical applications. However, multivariate sEMG analysis
is complicated by the fact that data recorded during dynamic
contractions are inherently nonstationary. To model this nonsta-
tionarity and to determine the dynamic muscle activity patterns
during reaching movements, we propose combining hidden
Markov models (HMMs) and multivariate autoregressive (mAR)
models into a joint HMM-mAR framework. We further propose
constructing muscle networks statistically by performing a second
level, group analysis on the subject-specific models. Network
structural features are subsequently investigated as input features
for the purpose of classification. The proposed approach was ap-
plied to real sEMG recordings collected from healthy and stroke
subjects during reaching movements. When examining group
muscle networks, we note that specific muscle connection patterns
were selectively recruited during reaching movements and were
differentially recruited after stroke compared to healthy subjects.
As the analysis was performed on the raw data, the amplitude
and the underlying “carrier data” of sEMG signals, we notice
that the HMM-mAR model fits the amplitude data well, but not
the raw or carrier data. The proposed sEMG analysis framework
represents a fundamental departure from existing methods where
only the amplitude is typically analyzed or the mAR coefficients
are directly used for classification. As the method may provide
additional insights into motor control, it appears a promising
approach warranting further study.
Index Terms—Classification tree, expectation maximization
(EM) algorithm, hidden Markov model (HMM), multivariate
autoregressive (mAR) model, stroke, surface electromyography
(sEMG).
I. INTRODUCTION
T
HE SURFACE ELECTROMYOGRAPHIC (sEMG)
signal is a semistochastic signal whose properties depend
upon a number of factors including the anatomical and phys-
iological properties of the contracting muscle, the amount of
subcutaneous fat, and choice of electrodes [1]. Since sEMG
Manuscript received April 19, 2007; revised March 8, 2008. The associate
editor coordinating the review of this manuscript and approving it for publica-
tion was Dr. Yonina C. Eldar.
J. Chiang and Z. J. Wang are with the Department of Electrical and Computer
Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
(e-mail: joycehc@interchange.ubc.ca; zjanew@ece.ubc.ca).
M. J. McKeown is with the Pacific Parkinson’s Research Centre, University of
British Columbia, Vancouver, BC V6T 2B5, Canada (e-mail: mmckeown@in-
terchange.ubc.ca).
Digital Object Identifier 10.1109/TSP.2008.925246
reflects underlying muscle activity and allows researchers to
noninvasively record several muscles simultaneously, it has
been widely investigated in the area of motor behavior.
A topic of increasing interest in motor control is to determine
how different muscles efficiently collaborate or interact together
during natural movements. Though traditionally sEMG record-
ings are widely examined in a univariate fashion, recent studies
suggest that sEMGs recorded from spatially distributed muscles
are correlated with each other [2]. Consistent with long-standing
clinical observations, this has led to the concept of synergies [3],
that is, coordinated activation of groups of muscles. It is sug-
gested that the central nervous system (CNS) may integrate syn-
ergies, as opposed to individual muscles, to coordinate muscle
activity patterns.
In the past few years, several different methods have been
applied to noisy sEMG data to infer synergistic actions and re-
vealed meaningful interactions between muscles, such as prin-
cipal component analysis (PCA), linear independent component
analysis (ICA) [2], [4], and nonnegative matrix factorization
(NMF) [5]. These partially linear decomposition methods op-
erate on a common assumption of a smaller numbers of common
sources, meaning that a small set of source signals are upstream
of the muscles and produce the sEMG signals. They are char-
acterized by a number of latent variables, and thus the mul-
tivariate sEMG data can be represented by subspace projec-
tions. For example, ICA assumes that the observations are com-
binations of statistically independent components, and its ob-
jective is to find underlying sources. Here, we explore a dif-
ferent approach, multivariate autoregressive mAR modeling, to
directly represent interactions between muscles without using
latent variables. Methods such as P/ICA do not explicitly reveal
interactions but implicitly through underlying sources. Also,
models such as P/ICA are instantaneous models, excluding tem-
poral information and quantifying only instantaneous depen-
dencies. However, interactions between muscles may not be in-
stantaneous. The mAR process, widely applied for modeling
the temporal dynamics of multivariate systems, can characterize
interregional dependencies within multiple channels in terms
of the historical influence one variable has on another. As we
are working on sEMG multivariate time series, we propose in-
vestigating mAR model to deal with the temporal lag between
muscles. Thus the synergies extracted impart complementary
knowledge, as they include the temporal aspects of muscle co-
ordination compared to the instantaneous methods like P/ICA.
Another common assumption implied in models such as
P/ICA is that the muscle activity patterns are time-invariant
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