# A dual ensemble classifier used to recognise contaminated multi-channel EMG
and MMG signals in the control of upper limb bioprosthesis

Pawel Trajdos0000-0002-4337-6847 Corresponding Author. Email:
<EMAIL_ADDRESS>Marek Kurzynski0000-0002-0401-2725  Wroclaw
University of Science and Technology, Wybrzeze Wyspianskiego 27,
50-370,Wroclaw, Poland

###### Abstract

Myopotential pattern recognition to decode the intent of the user is the most
advanced approach to controlling a powered bioprosthesis. Unfortunately, many
factors make this a difficult problem and achieving acceptable recognition
quality in real-word conditions is a serious challenge. The aim of the paper
is to develop a recognition system that will mitigate factors related to
multimodality and multichannel recording of biosignals and their high
susceptibility to contamination. The proposed method involves the use of two
co-operating multiclassifier systems. The first system is composed of one-
class classifiers related to individual electromyographic (EMG) and
mechanomyographic (MMG) biosignal recording channels, and its task is to
recognise contaminated channels. The role of the second system is to recognise
the class of movement resulting from the patient’s intention. The ensemble
system consists of base classifiers using the representation (extracted
features) of biosignals from different channels. The system uses a dynamic
selection mechanism, eliminating those base classifiers that are associated
with biosignal channels that are recognised by the one-class ensemble system
as being contaminated. Experimental studies were conducted using signals from
an able-bodied person with simulation of amputation. The results obtained
allow us to reject the null hypothesis that the application of the dual
ensemble foes not lead to improved classification quality.

123

##  1 Introduction

The loss of a hand significantly worsens the quality of a human’s life.
Although hand transplantology is making great progress, it is still not a
widely used medical procedure [15]. An alternative is to equip the subject
with a so-called bionic upper limb prosthesis, i.e. a prosthesis controlled by
biological signals. In bioprosthetic control, the subject’s intention to move
the prosthesis is encoded in the contractions of the residual stump muscles
that are still under the control of the motor cortex. Muscle activity
generates electromiographic (EMG) and mechanomiographic (MMG) biosignals that
can be recorded from the body surface and transferred to the prosthesis. Then,
the recorded biosignals, processed in accordance with the decision-making
control algorithm, constitute the basis for the operation of the kinematic
controler. The task of the kinematic controller is to control the DoFs of the
prosthesis in such a way that the movement of the mechanical structure
(trajectory of movement) ends with the posture of the prosthesis (grip or
manipulation) consistent with the intention of the subject.

During the past few decades, there has been a tremendous development in
pattern recognition-based control methods for bionic upper limb prostheses. In
this approach, the patient’s intention denotes the object being recognised,
the recorded biosignals constitute a formal representation of the object, and
the type of movement of the prosthesis is the class label. Numerous papers
covering a wide range of topics, such as the use of various classification
models and feature engineering procedures (feature extraction and feature
dimensionality reduction), are summarised in synthetic review publications and
comprehensive comparative analyses [28, 24, 4]. The effectiveness of complex
classification methods and recognition systems with different structures and
decision schemes was also investigated in this application area [18, 33, 1].
Although pattern recognition-based upper limb prosthesis control is considered
the most mature and advanced method, this does not translate into applications
in commercial bioprostheses. Conventional control methods still dominate here,
such as a simple on-off scheme with possible manual or semi-automatic
switching between prosthesis DoFs or an extended proportional control method
by measuring the average amplitude of biosignals [7]. This is because the task
of pattern recognition to control a bionic prosthetic hand is a difficult
problem. There are many factors that make it difficult to obtain an acceptable
classification quality in real conditions, allowing the amputee to use the
prosthesis in everyday activities. The most important of these factors are
[11, 19]:

  1. 1.

The multimodal nature of the formal representation of an object (typically:
multi-channel EMG and MMG biosignals, less frequently: other biosignals (EEG),
data from extra sensors like accelerometers, magnetometers, gyroscopes, scene
images from cameras),

  2. 2.

Difficulties in obtaining a sufficient set of training data (in one session)
due to phantom pain and postoperative pain as a result of amputation,

  3. 3.

Time-varying (nonstationary) recorded biosignals, the most common causes:
muscle fatigue, electrode schifts, changes of arm posture, changes of
elctrode/skin impedance (sweating), doffing/donning,

  4. 4.

Possibility of incorrect labelling of learning objects by the amputee
(reasons: misleading images of movements in control based on the paradigm of
phantom motor execution with non-biomimetic (arbitrary) strategy, it is
impossible to observe the movement of the amputated limb (phantom hand)),

  5. 5.

Poor intrasubject repeatability (changes due to human motor
learning/adaptation of the user to the control of the prosthesis) – more
generally denotes concept drift (different causes that could happen over the
period of some time),

  6. 6.

Contamination of biosignals: three types of signal contaminants: (1) noise
(thermal and flicker noise, amplifier saturation, analog to digital signal
clipping, quantisation noise), (2) interference (power line, ECG, crosstalk),
(3) artefacts (measurement artefacts, baseline wander, motion artefact, poor
electrode placement),

  7. 7.

A large number of primary features extracted from multimodal and multichannel
biosignals,

  8. 8.

The control system should produce a prediction of the intended movement in
real time (max delay < 200 ms).

The purpose of the paper is to develop a recognition system that will mitigate
three factors (factor 1 limited to EMG and MMG biosignals, factor 6 and factor
7) from those mentioned above. The proposed method involves the use of two co-
operating multiclassifier systems that have different structures and purposes.
The first system is composed of one-class classifiers related to individual
EMG and MMG biosignal recording channels, and its task is to recognise
(detect) contaminated channels. The aim of the second multiclassifier system
is to recognise the class of movement resulting from the patient’s intention
and represented by the recorded multichannel biosignals. The system consists
of base classifiers using the representation (extracted features) of
biosignals from different channels, which allows for taking into account
inter-channel dependencies between signals in the recognition process. The
system uses a negative dynamic selection mechanism, eliminating those base
classifiers that are associated with biosignal channels recognised by the one-
class ensemble system as being contaminated.

The main research questions that are to be answered are as follows:

  * •

RQ1 Does the proposed method perform better than the ensemble that always
selects all base classifiers?

  * •

RQ2 Does the proposed method perform better than a simple classifier trained
on the entire feature space?

  * •

RQ3 Does the proposed method perform better than the alternative approaches
presented in the literature?

  * •

RQ4 How do the investigated methods perform under different values of signal-
to-noise ratio?

  * •

RQ5 What is the impact of the number of EMG and MMG channels used to build the
ensemble.

The remainder of the article is organised as follows. In Section 2 we present
works related to the issue discussed in this paper. Section 3 contains a
comprehensive description of the proposed method. In Section 4, which concerns
experimental research, we present the signalset, the acquisition method of the
set, the comparative studies protocol, the extraction methods, the selection
of features, and classifier models. The results obtained are presented and
discussed in Section 5. Finally, concluding remarks are presented in Section
6.

##  2 Related Works

The quality of the signals (MMG, EMG) is crucial in the task of controlling a
bionic hand prosthetic device. When signal quality degrades, due to external
(environmental) or internal factors (e.g. muscle fatigue), controlling the
device becomes more difficult [20, 6]. Multiple solutions have been proposed
in the literature to address this issue.

The first category is to construct better hardware that is more robust to
noise and artefacts. Roland et al. proposed the use of flexible insulated
capacitive sensors that are less susceptible to losing contact with the skin
[26]. Another approach involves utilising circular electrodes that are not
affected by rotations. However, these sensors are still prone to electrode
shift [37]. For MMG signals, better quality microphones or accelerometers can
be used [20]. For high density EMG signals, there are also methods that
reconstruct signals from noise-affected signals using signals from
neighbouring sensors [6].

The next category is to filter out any artefacts that can appear at raw
(timeseries) signal level. Some approaches from this group use expert
knowledge to filter out predefined types of noise i.e. power line disturbances
[34, 3], noises comming from electrical activity of heart [3] or low frequency
motion artefacts [35, 26]. Other uses more general filtering approaches, such
as multiscale PCA [31], or variational mode decomposition [20, 2].

The third category consists of methods that utilise machine learning to deal
with signal disturbances. The methods in this category can be subdivided into
more subcategories. The first subgroup contains methods exclusively aimed at
detecting disturbed signals and stopping the prosthesis from performing the
movement based on faulty signals [5]. Multiclass classifiers can detect
contaminated signals, but it is crucial that contaminated and labelled
patterns are present in the training dataset [13]. This kind of method can use
different classifiers to detect signal contamination, i.e. SVM [13], or
various types of neural networks [22]. However, it requires prediction of the
types of noise patterns before using expert knowledge. Consequently, these
types of methods can only detect certain types of contamination, while the
other types remain undetected. To overcome this limitation, one-class
classification can be used. This kind of machine learning is designed to
detect outlier samples when the training set is composed only of
uncontaminated signals. For example, the method proposed by Freaser et al.
detects noisy channels using one-class SVM classifier [8]. Contaminated
signals can also be detected and used to alter the main classification
system’s working principle. Furukawa et al. proposed a multiclassifier system
that allows one EMG channel to be contaminated [12]. For an eight-channel EMG
signal, they trained an ensemble containing eight different classifiers. Each
of them uses only seven channels. When one of the channels is contaminated, a
proper seven-channel classifier is used. They also cover the case where no
contamination is detected. In that case, a classifier built using all eight
EMG channels is used. Some researchers propose to retrain the entire
classification system when spoilt channels are detected. However, this
approach is not very practical due to the large number of retraining actions
that may need to be taken [25]. These systems are used primarily in situations
where a sensor fault is permanent. So, the retraining procedure occurs rarely.
Researchers developing this kind of algorithms aim at accurate detection of
faulty sensors and shorten the retraining time [25]. On the other hand, a
classifier system that does not need explicit noisy channel detection may also
be proposed. An example is to simply use a robust classification ensemble such
as an error-correcting output code-based classifier [27]. The other is to use
noise-augmented data to build a robust classification system [21].

In this paper, we propose a multiclassifier system with a dynamic ensemble
selection strategy driven by the output of a one-class classifier-based
detector of noisy signal channels. The proposed method can be seen as a
generalisation of the method proposed in [12].

##  3 Proposed Method

Let us consider a system for the control of a bionic upper limb prosthesis
based on the multichannel EMG and MMG signals recognition scheme. Let

$\mathcal{C}=\mathcal{C}_{EMG}\cup\mathcal{C}_{MMG}=\\{C_{1},C_{2},\ldots,C_{2L}\\}$
(1)

denotes the set of EMG and MMG signals recorded from $2L$ sensors (channels)
located on the patient’s forearm stump. We assume the same number of channels
($L$) for both biosignals, because the EMG and MMG sensors are typically
placed in pairs in a common housing evenly spaced around the forearm.

The signals (1) represent the patient’s intention to perform a specific
movement (grip or manipulation) by the prosthesis. Control of the prosthesis
in amputees is based on the phantom motor execution (PME) paradigm, i.e. the
image of movement of a phantom hand ("movement without movement") that cannot
be observed [9]. Therefore, only the user knows what intention of the
prosthesis movement (what class) the recorded signals represent. Moreover, the
user has complete freedom in defining the meaning of classes so that they are
of practical importance and will be useful in everyday life. For this reason,
the intention of the movement (meaning of the class) is irrelevant at the
classification stage. This meaning will be determined at the stage of the
interpretation of the classification result, i.e. in the kinematic controller.
Therefore, we can label classes in a general way, for example using
consecutive natural numbers.

Let then

$\mathcal{M}=\\{1,2,\ldots,M\\}$ (2)

denotes a set of class numbers (labels). The number of classes $M$ for each
user may be different, as it is related to the size of the PME repertoire and
the user’s ability to activate the stump muscles.

For each channel, a feature extraction and a feature dimensionality reduction
procedures are applied that collectively transform the recorded signal $C_{l}$
into a feature vector $x_{l}$ in the $d_{l}$ dimensional feature space
$\mathcal{X}_{l}\subseteq\mathbb{R}^{d_{l}}(l=1,2,\ldots,2L)$. Many methods
and techniques have been used to extract time series features in the
bioprosthesis control task with varying success [14]. In experimental studies
(Section 4) features were extracted using the discrete wavelet transform
(DWT).

We assume that biosignals (1) can be contaminated with noise during the
acquisition process. Contaminations can appear randomly in different biosignal
channels, so we do not know in advance how many and which channels are
contaminated. Our goal is to develop a robust recognition system that will
identify contaminated channels and use this information to improve the
performance of classification algorithms. The proposed system consists of two
co-operating ensemble classifiers, the description of which is presented
below.

###  3.1 Ensemble of one-class classifiers

The first multiclassifier system consists of an ensemble of base classifiers:

$\Phi=\\{\phi_{1},\phi_{2},\ldots,\phi_{2L}\\}.$ (3)

The base classifier $\phi_{l}(x_{l})$ ($l=1,2,\ldots,2L$) is one-class
classifier which operates in the space $\mathcal{X}_{l}$ of features $x_{l}$
extracted from the biosignal $C_{l}$ registered in the $l$th channel.

The prediction of $\phi_{l}(x_{l})$ may be zero or one. Zero indicates that
$x_{l}$ is an outlier and the corresponding channel-specific signal $C_{l}$ is
recognised as contaminated with some kind of noise. Consequently, the
prediction equal to one indicates that $x_{l}$ is recognised as a target class
object, i.e., the corresponding biosignal $C_{l}$ is considered free of
contaminants. Each base classifier $\phi_{l}\in\Phi$ is trained using a
channel-specific training set $\mathcal{T}^{\phi}_{l}$ that contains only
objects of target class without the presence of outliers. This is the usual
way to build one-class classifiers [30]. This is because the one-class
classifiers build only a model of the target class that is capable of
detecting examples that do not belong to this class. In our study, target
class objects are the EMG and MMG signals registered under laboratory
conditions. Since the recording conditions are strictly controlled during the
experiment, all in-laboratory registered signals are assumed to be
noise/disturbance free. This approach is used in other work related to the
detection of EMG and MMG signal contamination [8].

###  3.2 Multiclassifier with a dynamic selection procedure

The second multiclassifier system:

$\Psi_{K}=\\{\psi^{(1)}_{K},\psi^{(2)}_{K},\ldots,\psi^{(|\Psi_{K}|)}_{K}\\}$
(4)

is designed to recognise the class of prosthesis movement from the set (2) in
accordance with the patient’s intention. All base classifiers $\psi_{K}^{(k)}$
of the system (4) use $K\in\\{1,2,\ldots,2L\\}$ EMG or MMG signals from the
set $\mathcal{C}$. The index $k$ is connected to the subset of $K$ signals
$\mathcal{C}^{(k)}_{K}\subset\mathcal{C}$. We suppose that the set (4) is a
complete one, therefore the cardinality of the multiclassifier system
$\Psi_{K}$ (the number of base classifiers in (4)) is equal to the number of
$K$-combinations of the set of $2L$ channels, that is:

$|\Psi_{K}|=\binom{2L}{K}=\frac{(2L)!}{K!(2L-K)!}.$ (5)

The joint feature space that each base classifier $\psi^{(k)}_{K}$ operates in
is defined as a Cartesian product of channel-related feature spaces:

$\mathcal{X}^{(k)}_{K}=\left(\bigtimes_{l:C_{l}\in\mathcal{C}^{(k)}_{K}}\mathcal{X}_{l}\right)\subseteq\mathbb{R}^{d^{(k)}_{K}}.$
(6)

In other words, vector $x^{(k)}_{K}$ is a concatenation of channel-specific
attribute vectors:

$x^{(k)}_{K}=\operatorname*{\scalerel*{\|}{\sum}}_{l:C_{l}\in\mathcal{C}^{(k)}_{K}}x_{l}.$
(7)

The prediction for an object $x^{(k)}_{K}\in\mathcal{X}^{(k)}_{K}$ is denoted
as $\psi^{(k)}_{K}(x^{(k)}_{K})\in\mathcal{M}$. Each base classifier
$\psi^{(k)}_{K}$ is trained using a supervised training procedure that employs
a base classifier-specific training set $\mathcal{T}_{\psi^{(k)}_{K}}$ [17].

Channel-specific signals that contain some amount of noise may have a negative
affect on the classification quality of the classifiers. Therefore, our goal
is to exclude from the ensemble base classifiers whose input space (6)
contains attributes coming from noise-contaminated channels. The exclusion is
made using responses from the one-class classifiers committee $\Phi$. The
following dynamic ensemble selection rule is applied:

$S(\psi^{(k)}_{K},x^{(k)}_{K})=\left\llbracket{\prod_{l:C_{l}\in\mathcal{C}^{(k)}_{K}}\phi_{l}(x_{l})=1}\right\rrbracket,$
(8)

where $\left\llbracket{\cdot}\right\rrbracket$ is the Iverson bracket operator
that returns true when the logical expression inside it is true. This rule
selects the ensemble members for which all channels are marked as the target
class. In the extreme case where none of the $\psi^{(k)}_{K}$ classifiers is
selected by rule
$S(\psi^{(k)}_{K},x^{(k)}_{K})\;\;\forall\psi^{(k)}_{K}\in\Psi_{K}$, all the
base classifiers of $\Psi_{K}$ are selected. The majority voting rule is used
to produce the final prediction of the ensemble after selecting the base
classifiers of the ensemble [17].

##  4 Experimental Setup

The experimental study is conducted to answer the research questions posed in
Section 1. To do so, we compared the following methods:

  * •

B: A single classifier trained on the data that comes from all available EMG
and MMG channels.

  * •

EC: Error correcting output codes ensemble trained on the data that comes from
all available EMG and MMG channels [27]. In this work, a simpler approach than
that presented in [27] is used. The reason for this is to use a base model
that is not partial least squares. We considered the following values of
code_size parameter $\\{2,3,4,5,6\\}$ The parameters are tuned with simple
search approach, using three-fold cross-validation.

  * •

Or: An oracle ensemble $\Psi_{K}$ built using given $K$-sized channel groups.
This reference method tells us whether at least one of the base classifiers of
the ensemble predicted the correct class for a given test sample.

  * •

Fu: An ensemble that always selects all base classifiers from $\Psi_{K}$. This
reference method tells us if the proposed dynamic committee selection
procedure allows for some improvement.

  * •

DO7: A seven channel ensemble, with a default model, which is described in
[12].

  * •

DO: The proposed method.

The experiments were carried out using signals obtained from a male able-body
subject, aged 73, right-handed. When creating the set of signals, the
amputation was mimicked by completely immobilising the hand during the
recording of the signals, which obliges the subject to generate EMG/EMG
signals based on his own image of the movement performed, not on the basis of
actual movements performed by the hand [29, 16]. The biosignals were
registered using a special designed measuring circuit with 4 EMG sensors and 4
MMG sensors (L=4) evenly spaced around the forearm and a sampling frequency of
1000 Hz. The detailed description of the measuring circuit is described in
[36]. The signalset used in the experiments consisted of eight classes
(according to the subject’s imagination): (1) wrist flexion, (2) wrist
extension, (3) ulnar deviation, (4) radial deviation, (5) index and middle
fingers flexion, (6) index and middle fingers extension, (7) ring and little
fingers flexion, (8) ring and little fingers extension. One hundred four-
channel EMG and four-channel MMG signals per class were recorded. Each
measurement lasted 1000 ms and was preceded with a 3 s break. Figure 1 shows
the placements of the sensor and the hand immobilisation technique. The
subject gave his informed consent prior to participation.

For the proposed methods, the Random Forest classifier is used as the base
classifier. The size of the Random Forest Ensemble is set to 30. The ensembles
are homogeneous. It means that for the ensemble, only one classification
algorithm (Random Forest) is used as the base classifier. As an outlier
detector, we use a one-class SVM classifier. This classifier proved to be a
useful tool in the task of detecting contaminated EMG signals [8]. The $\nu$
parameter of this classifier is tuned using the following procedure. Using a
threefold cross-validation procedure, the training and validation sets are
extracted. The validation (testing) part is then augmented with artificial
examples marked as noisy ones. Artificial examples are generated using a
uniform distribution in the classifier-specific input space $\mathcal{X}_{l}$.
The following values of $\nu$ are considered $\\{0.1,0.2,\ldots,1.0\\}$. The
classification quality is assessed using the balanced accuracy criterion
(binary classification task). When the best value of $\nu$ is found, the final
one-class classifier is trained using the entire training set
$\mathcal{T}^{\phi}_{l}$. We use the base classifiers implemented in the
scikit-learn package. Unless otherwise specified, the classifier parameters
are set to their default values.

To simulate real-world EMG and MMG signal contaminations, the following noise
generation techniques are used [23, 35, 6, 3]:

  * •

Simulation of power grid noise by injection of a sinusoidal signal whose
frequency varies from 48 to 52 Hz. The amplitude of the inserted noise depends
on the SNR rate considered in the experimental scenario. This kind of noise
may affect both EMG and MMG signals.

  * •

Signal attenuation that simulates the sensor losing contact with the skin. For
MMG signals, it simulates the situation when the distance between the
microphone and the skin increases. The attenuation level depends on the
selected SNR.

  * •

Gaussian noise. It simulates the general noises that may appear in the signal
acquisition circuit. This kind of noise may affect both EMG and MMG signals.

  * •

Simulation of non-linear amplifier characteristics for signals of high
amplitude. This is done by non-linear clipping the peaks of the signal. This
kind of noise may affect both EMG and MMG signals. The clipping level depends
on the selected SNR.

  * •

Baseline wandering. This is simulated by injecting low-frequency (0.5 to 1.5
Hz) sinusoidal noise. The amplitude of the signal depends on the selected SNR.
For MMG signals, frequencies coming from this interval simulate motion
artefacts.

In experimental studies, we consider the following SNR levels
$\\{0,1,2,\ldots,6,10\\}$.

The training and testing sets are obtained by a ten-fold cross-validation
repeated 4 times. The testing dataset is then randomly contaminated with one
of the above-mentioned noise types with a selected SNR level. The number of
contaminated channels is also randomly selected from the following set of
values $\\{1,2,\ldots,7\\}$. The number of channels used to create base
classifiers of the $\Psi_{K}$ ensemble is
$K\in\\{1,2,3,\ldots,7,\\{2,3,4\\},\\{3,4,5\\},\\{2,3,5\\},\\{2,4,5\\}\\}$. In
the above-mentioned set, subsets like $\\{2,3,4\\}$ mean that the ensemble
contains all base classifiers for the mentioned numbers of channels. In other
words, a joint ensemble is built that aggregates the base classifiers coming
from the ensembles built for the considered values of $K$.

Feature vectors were created from raw EMG and MMG signals using the discrete
wavelet transform technique. The db6 wavelet and three levels of decomposition
were used. The following functions were calculated for the transformation
coefficients [14]: MAV (mean absolute value), SSC (slope sign change). Due to
the relatively small sample bot experiments were performed on the same
dataset.

Figure 1: Illustration of recording EMG and MMG signals.

Following the recommendations of [10], the statistical significance of the
results obtained was evaluated using the pairwise Wilcoxon signed rank test.
Since multiple comparisons were made, family-wise errors (FWER) should be
controlled. To do so, Holm’s procedure of controlling the FWER was employed.
For all tests, the significance level was set to $\alpha=0.05$. We used
statistical tests and correction procedures implemented in SciPy. For some
analysis, the average rank approach is also used. To assess the classification
quality, the balanced accuracy criterion is employed. The experimental code is
provided in 111https://github.com/ptrajdos/CLDD_2024.git

##  5 Results and discussion

Let us begin with an experiment that examines how changing $K$ affects the
classification quality of the ensemble methods. During the experiment, the
following values are investigated:
$K\in\\{1,2,3,\ldots,7,\\{2,3,4\\},\\{3,4,5\\},\\{2,3,5\\},\\{2,4,5\\}\\}$. In
Figures 2, 3 and Tables 1, 2 the above-mentioned values of $K$ are denoted
using natural numbers $\\{1,2,\ldots,11\\}$. If $K$ is represented as a set,
it means that we investigate the joint committee created using the mentioned
values of $K$. Figures 2 and 3 present the averaged ranks (averaged over
different SNR values and different folds) related to different $K$ values for
each investigated ensemble method. In other words, for each method the values
of $K$ are ranked. Tables 1 and 2 present the average ranks and the outcome of
the statistical test performed. Each row of the table presents the average
ranks related to an ensemble method, the name of which is presented in the
first column. Each of the remaining columns is related to different values of
$K$ used to create the ensemble. The subscript numbers below the average rank
value present the column numbers for the methods to which the method with the
selected value of $K$ is significantly better. When there are no significant
differences between the column of interest and the other columns, a pause sign
‘–’ is placed in the subscript.

We start with experiments conducted on mixture of clean and noisy signals. It
is evident from the Figure 2 and the Table 1 that the classification quality
obtained by each of the ensemble methods is strongly influenced by $K$.
Compared to other values of $K$, all ensemble methods perform poorly for $K=1$
(one classifier for one EMG or MMG channel). This is because different muscles
are activated in a different way when the subject generates different
contraction patterns. Consequently, a lot of information about the muscle
activation performed is encoded in differences between channels [32]. Even for
$K=2$, the increase in classification quality is significant compared to
$K=1$. An interesting result may be observed for the oracle classifier (Or)
when ensembles are built only for a single value of $K$. The best performance
(in terms of average ranks) is observed when $K=3$. However, there are no
significant differences between $K\in\\{2,3,4\\}$. When the value of $K$
increases over 4, the average rank decreases significantly. Since the oracle
algorithm selects the correct class if one is presented in the ensemble, the
drop in classification quality means that the diversity of the ensemble is the
highest for $K\in{2,3,4}$ and then drops. The diversity is then clearly
related to the size of the ensemble $|\Psi_{K}|$. However, the size of the
ensemble is not the only factor that affects the performance of the
classifiers. If the ensemble size was only factor, then, for a single value
$K$, the best performance should be observed for $K=4$ since the ensemble size
is the highest for this value. When the ensemble is built using more signal
channels, then the base classifiers become less diverse since they share more
channel-specific information. When multiple values of $K$ are used to build a
joint ensemble, the performance of the oracle classifier is also high due to
the high diversity. A similar pattern of average ranks can be observed for the
ensemble that always selects all base classifier Fu. For this type of
ensemble, diversity also plays an important role, as the best results are
obtained for committees containing a relatively large number of classifiers
$K\in\\{2,3,4,5\\}$. For the proposed method, on the other hand, no
significant differences can be observed for $K\in\\{3,4,5,6,7\\}$. For those
values of $K$, the differences between the average ranks are also smaller and
do not decrease if $K$ increases. This means that even if the committee is
smaller and less diverse, the outlier selection procedure successfully
eliminates the base classifiers related to noisy channels. Consequently, the
classification quality does not drop.

Now, we analyse the situation where there is almost no artificial noise
(contamination) in the test signals (SNR=10). The results are presented in
Figure 3 and Table 2. The behaviour of the Or and Fu methods is quite similar
when there is no noise present. That is, the methods perform better when the
size and diversity of the ensemble is high. Joining the committees built for
different values of $K$ has a positive impact on the quality of
classification. The behaviour of the proposed method DO, on the other hand,
changes significantly. That is, the classification quality continues to
increase when higher values of $K$ are considered. Even if the signals are not
contaminated with artificial noise, the removal of some base classifiers from
the committee allows the classification quality to be increased. This may mean
that even signals registered under strictly controlled laboratory conditions
may contain some degree of noise that is successfully detected by the outlier
detectors. The quality of the classification can be improved by removing the
slightly contaminated channels. The increase in classification quality is also
related to the number of channels used to build each of the base classifiers.
The more channels we include, the better the classification quality. This is
due to the fact that important information about muscle activation pattern is
encoded in differences between signals registered for different muscles [32].
Even combining a larger number of simpler base classifiers cannot outperform
the results obtained by base classifiers built for a larger number of
channels. However, as the above-described results show, this effect holds only
for signals whose contamination level is relatively low. For signals with
injected artificial noise, more diverse ensembles are preferable. Taking this
into account, the joint ensembles that combine different values of $K$ should
combine smaller and larger values of $K$ to improve the classification quality
of clean signals.

Based on the results, it is recommended to establish joint committees for
various values of $K$. It is clear that for all the multiclassifier systems
considered, the joint committees offer the best classification quality. For
the second analysis performed, we use the build committees for $K=7$ (to
provide a better comparison with the reference method DO7) and $K=\\{2,3,5\\}$
to show the abilities of the joint committees built for different values of
$K$.

Figure 2: The impact of changing $K$, signal with noise – ranks. Table 1: The impact of changing $K$, signal with noise – statistical tests. | BAC
---|---
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11
Or | 2.025 | 6.934 | 7.305 | 7.072 | 5.375 | 3.539 | 1.336 | 8.342 | 7.767 | 8.086 | 8.219
| 7 | 1,5,6,7 | 1,5,6,7 | 1,5,6,7 | 1,6,7 | 1,7 | – | 1,2,3,4,5,6,7,9 | 1,2,3,4,5,6,7 | 1,2,3,4,5,6,7,9 | 1,2,3,4,5,6,7,9
Fu | 1.000 | 6.245 | 6.870 | 6.423 | 6.395 | 5.383 | 5.223 | 7.253 | 7.070 | 7.250 | 6.886
| – | 1,6,7 | 1,6,7 | 1,6,7 | 1,6,7 | 1 | 1 | 1,2,4,5,6,7 | 1,2,6,7 | 1,2,4,5,6,7 | 1,6,7
DO | 1.000 | 4.523 | 6.602 | 6.794 | 6.220 | 6.433 | 6.528 | 6.875 | 7.153 | 7.234 | 6.638
| – | 1 | 1,2 | 1,2 | 1,2 | 1,2 | 1,2 | 1,2 | 1,2,3,5,6,7 | 1,2,3,5,6,7,11 | 1,2
Figure 3: The impact of changing $K$, signal without noise – ranks. Table 2: The impact of changing $K$, signal without noise – statistical tests. | BAC
---|---
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11
Or | 1.500 | 6.825 | 6.888 | 7.138 | 6.287 | 4.787 | 1.837 | 7.588 | 7.600 | 7.812 | 7.737
| – | 1,6,7 | 1,6,7 | 1,6,7 | 1,7 | 1,7 | – | 1,6,7 | 1,6,7 | 1,5,6,7 | 1,6,7
Fu | 1.000 | 4.675 | 7.425 | 6.237 | 6.987 | 5.850 | 5.450 | 6.550 | 7.800 | 6.213 | 7.812
| – | 1 | 1,2 | 1 | 1,2 | 1 | 1 | 1,2 | 1,2 | 1 | 1,2,7
DO | 1.000 | 3.225 | 5.100 | 6.537 | 7.438 | 8.238 | 9.350 | 5.513 | 6.287 | 6.662 | 6.650
| – | 1 | 1,2 | 1,2 | 1,2,3 | 1,2,3,8,9 | 1,2,3,4,5,8,9,10,11 | 1,2 | 1,2 | 1,2 | 1,2

The results related to different SNR values are presented in Figures 4 – 5 and
Tables 3 – 4. Figures present method-related boxplots for different values of
SNR. Box plots are colour encoded. The tables present the method-related
average (over different folds) ranks for different values of SNR. Each row of
a table is related to different SNR values. Each column is related to a
different method. Subscripts related below each average ranks contain indices
of methods (number of columns) that given method is significantly better.

Let us start with the results related to $K=7$. As shown in Figure 4 and Table
4, it is evident that the classification quality of all investigated methods
increases with increasing SNR. This is clear because higher values of SNR mean
that less noise is present in the signals. The oracle classifier is
undoubtedly the classifier with the highest-quality classification. This
classifier is a perfect committee selection procedure that possesses the
information about the true class of the object. Its superior performance over
B and EC shows that the proposed method of ensemble creation has a great
potential that can be revealed by a proper committee selection technique. On
the other hand, Fu represents the most naive committee selection technique
that always uses the full ensemble to make a prediction. Despite of its
simplicity Fu method in some cases outperforms B method. This is further
confirmation that the proposed method of committee creation has a great
potential, since it is outperformed only by EC for $\mathrm{SNR}=10$. However,
a committee selection procedure plays the most important role since an
improper selection procedure can worsen the classification quality. For our
experiment, the selection rule used by DO7 does not perform very well. It is
unable to outperform any other of the investigated methods and, more
importantly, it is often outperformed by Fu, DO and EC. This is due to the DO7
method being designed in such a way that it always selects only one classifier
from the ensemble. The selected classifier may be a classifier trained on the
entire dataset (no-noise detected by one-class classifiers) or a dateset with
one channel removed. The assumption that there can be only one noisy channel
is overoptimistic, since in real-world data, more channels may be noisy. This
is why our more general method seems to perform better than DO7. The committee
selection method proposed in this paper (DO) is often better than B and, in
general, is comparable to Fu and EC. Being comparable to Fu is not a great
advantage, since the proposed method uses an additional one-class committee
that results in a higher computational burden.

Figure 4: The impact of changing SNR, $K=7$ – boxplots. Table 3: The impact of changing SNR, $K=7$ – statistical tests. | BAC
---|---
| B | EC | Or | Fu | DO | DO7
SNR:10 | 2.788 | 4.188 | 5.875 | 3.375 | 3.038 | 1.738
| 6 | 1,4,5,6 | 1,2,4,5,6 | 6 | 6 | –
SNR:6 | 1.988 | 3.862 | 6.000 | 3.550 | 3.300 | 2.300
| – | 1,6 | 1,2,4,5,6 | 1,6 | 1,6 | –
SNR:5 | 2.350 | 3.962 | 6.000 | 3.475 | 3.288 | 1.925
| – | 1,6 | 1,2,4,5,6 | 1,6 | 1,6 | –
SNR:4 | 2.263 | 3.712 | 6.000 | 3.638 | 3.163 | 2.225
| – | 1,6 | 1,2,4,5,6 | 1,6 | 1,6 | –
SNR:3 | 2.325 | 3.750 | 6.000 | 3.237 | 3.288 | 2.400
| – | 1,6 | 1,2,4,5,6 | 1,6 | 1,6 | –
SNR:2 | 2.562 | 3.725 | 6.000 | 2.888 | 3.188 | 2.638
| – | 1,6 | 1,2,4,5,6 | – | – | –
SNR:1 | 2.663 | 3.587 | 5.987 | 3.450 | 2.513 | 2.800
| – | 1,5 | 1,2,4,5,6 | 5 | – | –
SNR:0 | 2.612 | 3.425 | 6.000 | 3.175 | 2.712 | 3.075
| – | 1 | 1,2,4,5,6 | – | – | –

Fortunately, the situation changes when the size of the initial committee and
its diversification increase. This case occurs for $K\in\\{2,3,5\\}$. For this
experiment, the Or classifier achieved almost constant classification quality,
approximately equal to $1.0$. This means that with proper committee selection
procedures, the potential of the committee is great. The naive selection
procedure used by Fu also allows it to be one of the best performing methods
in this comparison, as it outperforms B and OD7. It is also comparable to EC.
In this experimental scenario, the proposed method exhibits a different
behaviour. For low SNR values (0, 1), it outperforms B, EC, Fu and DO7. This
means that for low SNR values, the removal of noisy channels offers a great
improvement. However, the positive differences between DO and remaining
methods disappear when the SNR increases. For high SNR values, the proposed
method is outperformed by EC and Fu (for $\mathrm{SNR}=10$ also by B). This
leads to the conclusion that the complete removal of noisy channels is
beneficial for a large amount of noise in these channels. However, when the
amount of noise is low, the base classifiers of the ensemble are robust enough
to deal with this noise. Consequently, the selection of all classifiers within
the ensemble offers better classification quality. Therefore, in future work,
a new method of soft committee selection should be developed using the above-
mentioned observation in practice.

Figure 5: The impact of changing SNR, $K\in\\{2,3,5\\}$ – boxplots. Table 4: The impact of changing SNR, $K\in\\{2,3,5\\}$ – statistical tests. | BAC
---|---
| B | EC | Or | Fu | DO | DO7
SNR:10 | 2.788 | 4.287 | 6.000 | 3.825 | 1.875 | 2.225
| 5 | 1,5,6 | 1,2,4,5,6 | 1,5,6 | – | –
SNR:6 | 2.237 | 3.875 | 6.000 | 4.300 | 2.112 | 2.475
| – | 1,5,6 | 1,2,4,5,6 | 1,5,6 | – | –
SNR:5 | 2.225 | 3.600 | 6.000 | 4.400 | 2.350 | 2.425
| – | 1,5,6 | 1,2,4,5,6 | 1,2,5,6 | – | –
SNR:4 | 2.062 | 3.425 | 6.000 | 4.225 | 2.862 | 2.425
| – | 1,5,6 | 1,2,4,5,6 | 1,2,5,6 | – | –
SNR:3 | 1.750 | 3.087 | 6.000 | 4.025 | 3.737 | 2.400
| – | 1,6 | 1,2,4,5,6 | 1,2,6 | 1,6 | –
SNR:2 | 1.762 | 3.013 | 6.000 | 3.800 | 4.175 | 2.250
| – | 1,6 | 1,2,4,5,6 | 1,2,6 | 1,2,6 | –
SNR:1 | 1.950 | 2.888 | 6.000 | 3.538 | 4.588 | 2.038
| – | 1,6 | 1,2,4,5,6 | 1,6 | 1,2,4,6 | –
SNR:0 | 1.637 | 2.875 | 6.000 | 3.475 | 4.475 | 2.538
| – | 1 | 1,2,4,5,6 | 1,6 | 1,2,4,6 | 1

To summarise, the answers to the research questions are as follows:

  * •

RQ1 In general, the proposed method DO is comparable to Fu. In case of low SNR
the proposed method is better.

  * •

RQ2 The proposed DO method performs better than B classifier when the amount
of noise in signals is relatively high. When the amount of noise is low, then
the methods are comparable.

  * •

RQ3 The proposed DO method performs better than DO7 classifier when the amount
of noise in signals is relatively high. When the amount of noise is low, then
the methods are comparable.

  * •

RQ4 In general, the higher value of SNR is, the better the investigated
methods perform. However, the proposed method shows quite stable
classification quality results for low SNR values.

  * •

RQ5 In general, classification quality is more related to the ensemble size
and diversity rather than the number of the included channels. However, when
no noise is present, the greater number of channels (parameter $K$) is, the
classification quality is better.

##  6 Conclusions

In this paper, we propose a dual ensemble multiclassifier system that is
designed to deal with noise/artefacts in multimodal data consisting of EMG and
MMG signals. The first ensemble system is a one-class classifiers ensemble
responsible for detecting noisy/contaminated channels. A one-class classifier
ensemble is used to allow the ensemble to recognise any kind of outlying
signal. The output of a one-class ensemble is then used to perform dynamic
ensemble selection in the second multiclassifier system. The second
multiclassifier system contains base classifiers built using signals coming
from multiple channels. The number of channels used to create the base
classifier for this ensemble is a parameter of the system.

We performed two experiments. The first aims at determining the best value of
the above-mentioned parameter $K$. The goal is also to analyse the impact of
the ensemble size and diversity on the classification quality of the
ensembles. The first experiment shows that, in the presence of noise, ensemble
classifiers tend to provide higher quality predictions when the diversity of
the ensemble is higher. It also shows that it is desirable to join multiple
committees built for different values of the parameter $K$ since the diversity
of such committees is greater than an ensemble built for a single value of
$K$.

During the second experiment, we analyse how the proposed method performs when
the signal-to-noise ratio (SNR) changes. In this experiment, we also compare
the proposed method with selected reference methods. The results show that
with proper settings of the $K$ parameter, the proposed method can outperform
the reference methods for low SNR values (when the signals are noisy).
However, the superiority of the proposed method no longer holds for higher SNR
values. This is due to the partial robustness of the base classifiers (of
$\Psi_{K}$) to noise. For low-noise scenarios, it is better to select all base
classifiers from the ensemble.

These observations lead us to the conclusion that a new, better dynamic
ensemble selection procedure may be constructed. This new strategy should
completely remove ensemble classifiers that use channels with a high level of
contamination, but when the contamination degree is low, it should allow the
outcome of such classifiers to be used. Because of this, our future work is
aimed at developing such an ensemble selection procedure. We think that a soft
ensemble selection strategy should be suitable and meets the properties
mentioned above.

This work is supported by the National Center for Research and Development
(www.ncbr.gov.pl) through project no.  /0018/2020-00 within”Things are for
people” programme. The authors have no conflict of interest to declare. The
authors thank Dr. Andrzej Wolczowski for valuable discussions, Dr. Jerzy
Witkowski for the design and manufacture of EMG and MMG sensors and Dr. Michal
Bledowski for the application for recording EMG and MMG signals [36].

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