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### 隐马尔科夫模型与自回归结合在肌电数据分析中的应用 #### 引言表面肌电图（sEMG）作为评估肌肉激活的主要非侵入性手段，在临床和生物医学应用中占据核心地位。然而，多变量sEMG分析面临的一大挑战是动态收缩期间记录的数据固有的非平稳性。为了模拟这种非平稳性并确定在伸展运动过程中动态的肌肉活动模式，研究者提出了一种将隐马尔科夫模型（HMM）和多变量自回归模型（mAR）结合的联合框架——HMM-mAR网络框架。 #### HMM-mAR网络框架该框架的核心在于结合了两种强大的统计模型：隐马尔科夫模型和多变量自回归模型。HMM是一种用于处理时序数据的统计模型，特别适用于建模具有隐含状态序列的数据集，如肌肉的动态活动。另一方面，mAR模型则用于捕捉时间序列数据中的线性关系，能够揭示多个变量间的相互作用。当这两种模型被整合在一起时，它们能够更全面地解析sEMG信号中的复杂模式，包括肌肉活动的非平稳性和动态特性。 #### 构建肌肉网络研究者进一步提出了通过执行第二层级的群体分析来构建肌肉网络的统计方法。这一步骤涉及对个体特异性模型进行分组分析，以识别出肌肉之间的连接模式。这些网络结构特征随后被用作分类任务的输入特征。通过对健康个体和中风患者在伸展运动过程中的真实sEMG记录进行应用，研究者观察到特定的肌肉连接模式在伸展运动中被有选择地招募，并且在中风后与健康个体相比显示出不同的招募模式。 #### sEMG信号分析框架以往的方法通常仅分析sEMG信号的幅度或直接利用mAR系数进行分类，而提出的sEMG分析框架代表了对现有方法的根本性突破。值得注意的是，HMM-mAR模型能够很好地拟合sEMG信号的幅度数据，但不能拟合原始数据或所谓的“载体数据”。这一发现表明，HMM-mAR框架可能为运动控制机制提供额外的洞察，因此它被认为是一种值得进一步研究的有前景的方法。 #### 结论通过结合HMM和mAR模型，研究人员不仅能够有效地处理sEMG信号的非平稳特性，还能揭示肌肉活动模式在不同生理状态下的变化。这种方法对于理解健康和疾病状态下的肌肉功能、优化康复策略以及开发新的诊断工具具有重要意义。随着技术的不断发展，HMM-mAR框架有望成为分析和解释肌电数据的强大工具，促进神经科学和康复医学领域的发展。

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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

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

4070 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 56, NO. 8, AUGUST 2008

throughout the movements investigated. However, signiﬁcant

time-dependent correlations can be shown to exist between

muscle channels during most natural movements, suggesting

a complex interplay and coordination between muscles in

time-varying fashion. It is widely accepted that the sEMG

signals recorded from natural behaviors, such as reaching, as

opposed to isometric contractions, are nonstationary. Clin-

ically, reaching movements are considered to consist of an

initial phase, under “open loop” control, where feedback is less

critical, and a “closed loop” control phase, where feedback

is important [6]. In particular, in people with diseases of the

cerebellar hemispheres, initial portions of reaching movements

are smooth, but an intention tremor becomes prominent towards

the end of movements. The time-varying and nonstationary

properties implied by open-loop and closed-loop phases of

reaching suggests that techniques assuming stationarity (e.g.

coherence, linear component analysis) may result in mis-

leading interpretations. To address these concerns, a common

quasi-static approach is to incorporate a sliding time window

into the original signal models, such that the stationarity as-

sumption is valid in a piecewise sense. However, the selection

of an appropriate (possibly time-varying) window length is

a nontrivial task, and it can have a signiﬁcant effect on the

analysis results [7].

Based on the aforementioned observations, in this paper

we propose combining hidden Markov models (HMMs) and

multivariate autoregressive mAR models into an HMM-mAR

framework for modeling nonstationary multivariate sEMG

time series and determining dynamic muscle activity patterns

during reaching movements. HMM-mAR is advantageous for

modeling sEMG data for a number of reasons. First, an mAR

model allows full representation of multivariate sEMG signals,

so it naturally captures the dependency relationships between

different channels. The results can be explored further to reveal

muscle associations and synergies. Furthermore, given that

the data are nonstationary and we have no prior knowledge on

when the mAR models may change, incorporating HMM pro-

vides a probabilistically tractable and robust way of modeling

the dynamic changes of state (i.e., different mAR models) [8].

HMM-mAR, also known as AR model with Markov regime,

has been widely used in econometrics, target tracking, and

statistical signal processing [9], but has not been commonly ap-

plied to biophysiological data. Cassidy and Brown [10] applied

HMM-mAR to electrophysiological signals for the purpose

of spectral estimation. In the present paper, we extend prior

approaches to investigate the suitability of HMM-mAR for

sEMG signals and study dynamic interactions among muscles

during reaching.

In addition, we also explore different forms of sEMG data

for further analysis. A sEMG signal can be considered as a

zero-mean, band-limited, and wide-sense stationary stochastic

process (referred to as “carrier data” here) modulated by the

EMG amplitude [11], and it has been suggested that carrier data

can be approximately modeled as a Gaussian process. As it is

assumed that the amplitude data represent muscle activity from

numerous individual muscle ﬁbers, a common, traditional prac-

tice in the EMG literature is to focus on the amplitude of the

sEMG signal, which can be obtained by rectifying and low-pass

ﬁltering the raw sEMG signal, in effect discarding the carrier

data. Recently, an increasing number of studies have been re-

ported working on raw, unrectiﬁed sEMG signals. For instance,

linear ICA was applied to noisy raw sEMG data and revealed

meaningful interactions between muscles [4]. In [12], a mul-

tivariate autoregressive (mAR) model was explored to model

multichannel raw sEMG signals. To the best of our knowledge,

no previous studies have focused on the carrier data of sEMG

signals, yet our very recent study suggests that the carrier data

may also be informative [13]. In this paper, to have a better un-

derstanding of sEMG and its nature, we will use a fundamen-

tally different approach and model different forms of the sEMG

signals: raw sEMG, amplitude data and carrier data.

In real biomedical applications, it is commonly required to

extrapolate results from few subjects to an entire population

in order to explore, for example, changes in reaching move-

ments after stroke. The analysis requires methods to meaning-

fully integrate results from individual subjects and rigorously

compare the results across groups. To address this intersubject

variability issue, we employ statistical analysis to investigate

consistent muscle collaboration patterns across subjects within

a given subject group.

The main contributions of this paper are as follows:

• Presents an HMM-mAR framework for modeling the

muscle activities during reaching movements using sEMG

signals;

• Constructs muscle networks and suggests that structural

features appear robust to intersubject variability; and

• Investigates the results of model-ﬁtting when the proposed

analysis is performed on raw, amplitude and carrier data of

sEMG signals.

The paper is organized as follows. In Section II, we describe

the proposed HMM-mAR framework and discuss different

forms of sEMG signals. A classiﬁcation scheme is proposed

for classifying sEMG signals collected from healthy and stroke

subjects. The classiﬁcation results are discussed in Section III.

II. M

ETHODS

In this section, we ﬁrst describe the HMM-mAR framework,

whose state parameters, including mAR coefﬁcients, are esti-

mated using the expectation maximization (EM) algorithm. We

then introduce the amplitude-modulated model of sEMG signal.

Finally, we describe the process of constructing muscle net-

works and propose a classiﬁcation scheme based on the learned

HMM-mAR model. For the remainder of the paper, we use bold

letters to represent vectors and matrices.

A. HMM-mAR Model

We propose modeling the multichannel sEMG data

using a hidden Markov-model multivariate autoregressive

(HMM-mAR) process. An HMM-mAR model can be consid-

ered as a variant of a regular mAR model. The key difference

is that in HMM-mAR, the model parameters, including mAR

coefﬁcients and noise covariance, are no longer time-invariant,

but are modulated by an unobserved Markov chain. In other

words, the HMM-mAR model switches between different

“submodels,” each of which has its own set of parameters, and

thus the resulting time series is piecewise stationary. A good

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