**3. Analysis of simultaneous EMG and acceleration recordings in PD**

### **3.1. EMG and acceleration measurements**

We analyzed simultaneous EMG and acceleration measurements of PD patients and healthy subjects in [28, 29] and aimed to develop methods for discriminating between the patients and the healthy subjects on the basis of the measured signals. The signals were measured during isometric contraction of BB muscles [28] and during dynamic elbow flexion-extension movements [29].

During the isometric task, the subjects were asked to hold their elbows at a 90° angle with their palms up. During the dynamic task, the subjects were asked to flex and extend their both elbows vertically and freely in two-second cycles with their palms up. Surface EMGs were registered continuously from the BB muscles and the accelerations of forearms simultaneously from the palmar side of subject's wrists. All measurements were performed by using the ME6000 -biosignal monitor (Mega Electronics Ltd., Kuopio, Finland), disposable Ag/AgCl electrodes (Medicotest, model M-00-S, Ølstykke, Denmark) in bipolar connection and tri-axial accelerometers (Meac-x, Mega Electronics Ltd., range ±10 g). Signals were sampled with the rate of 1000 Hz. The resultant of the acceleration was used in the analysis. Low-frequency trends were removed from both signals by using the smoothness priors method [46]. The high-pass cut-off frequencies were 10 Hz for EMG and 2 Hz for acceleration.

Typical EMG and acceleration signals of one PD patient and one healthy subject during the isometric and dynamic task are presented in Figure 3. It is observed in the isometric A Perspective on Current Applications and Future Challenges Feature Extraction Methods for Studying Surface Electromyography and Kinematic Measurements in Parkinson's Disease <sup>7</sup> 227 Feature Extraction Methods for Studying Surface Electromyography and Kinematic Measurements in Parkinson's Disease

6 Will-be-set-by-IN-TECH

• The first eigenvector is the best mean-square fit for the feature vectors of all subjects. Thus, it is similar to the mean of all feature vectors. Therefore, the first PC describes the amplitude of the histogram and the CR expansion with respect to the mean of all subjects. • The second eigenvector is the best mean-square fit for the residual of the first fit. The second eigenvector describes variations in the peaks (modes) of the histograms and CR

• The third eigenvector models variations in the heights and widths of the histograms and

The rest of the eigenvectors contain information about higher frequencies of the data and do not interest us in this case. The biggest differences between patients and healthy subjects were found in the third PC and some differences were observed in the first PC. Therefore, the discrimination between subjects was performed with respect to the third and the first PC.

A linear discriminant was used in [32] for discriminating between the subjects in the two-dimensional feature space that was spanned by the third and the first PCs. The best discrimination results were obtained by using the augmented PC approach (see results in Figure 2). According to the results, 72 % of PD patients can be discriminated from 86 % of

We analyzed simultaneous EMG and acceleration measurements of PD patients and healthy subjects in [28, 29] and aimed to develop methods for discriminating between the patients and the healthy subjects on the basis of the measured signals. The signals were measured during isometric contraction of BB muscles [28] and during dynamic elbow flexion-extension

During the isometric task, the subjects were asked to hold their elbows at a 90° angle with their palms up. During the dynamic task, the subjects were asked to flex and extend their both elbows vertically and freely in two-second cycles with their palms up. Surface EMGs were registered continuously from the BB muscles and the accelerations of forearms simultaneously from the palmar side of subject's wrists. All measurements were performed by using the ME6000 -biosignal monitor (Mega Electronics Ltd., Kuopio, Finland), disposable Ag/AgCl electrodes (Medicotest, model M-00-S, Ølstykke, Denmark) in bipolar connection and tri-axial accelerometers (Meac-x, Mega Electronics Ltd., range ±10 g). Signals were sampled with the rate of 1000 Hz. The resultant of the acceleration was used in the analysis. Low-frequency trends were removed from both signals by using the smoothness priors method [46]. The

Typical EMG and acceleration signals of one PD patient and one healthy subject during the isometric and dynamic task are presented in Figure 3. It is observed in the isometric

high-pass cut-off frequencies were 10 Hz for EMG and 2 Hz for acceleration.

**3. Analysis of simultaneous EMG and acceleration recordings in PD**

expansions of all subjects.

**2.3. Results**

226

movements [29].

CR expansions in the whole data set.

Computational Intelligence in Electromyography Analysis –

healthy subjects on the basis of EMG signal morphology.

**3.1. EMG and acceleration measurements**

**Figure 3.** EMG and acceleration recordings of one PD patient (left) and one healthy subject (right) during the isometric and the dynamic task.

recording, that the EMG signal of the PD patient differs from the EMG signal of the healthy subject by containing recurring EMG bursts and the acceleration signal by containing regular high-amplitude oscillation. This oscillation is likely due to the resting and postural tremor. It is observed in the dynamic recording, that the EMG signal of the PD patient is characterized by recurring spikes and the acceleration recording by containing high-amplitude oscillation during the extension phases of the movement. The oscillation in the acceleration signal (which was high-pass-filtered with 2 Hz as cut-off frequency) is likely due to muscle rigidity and kinetic tremor (tremor that occurs during movement). In the flexion phases of the movement, the differences between the patient and the healthy subject are not as pronounced.

#### **3.2. Feature extraction from EMG and acceleration signals**

It was observed in [23] and [28, 29] that the conventional amplitude- and spectral-based EMG parameters (root mean square value and median frequency) are not effective in characterizing the EMG signals of PD patients in comparison to the signals of the healthy subjects. Therefore, we extracted a set of other PD characteristic signal features from the isometric [28] and dynamic EMG and acceleration recordings [29]. These parameters are detailed in Table 1 and they were calculated as epoch averages from the isometric EMG and acceleration signals and as time-varying from the dynamic signals.

228 Computational Intelligence in Electromyography Analysis – A Perspective on Current Applications and Future Challenges Feature Extraction Methods for Studying Surface Electromyography and Kinematic Measurements in Parkinson's Disease <sup>9</sup>


8 Will-be-set-by-IN-TECH

**Table 1.** PD characteristic signal features and their notations. The subscripts r and l in the notations stand for the side of the body.

#### *3.2.1. Parameters of surface EMG signal morphology*

In [28], we used two parameters (*k* and *cr*) for measuring the peakedness of EMG signals. The sample kurtosis was calculated as the fourth centered moment of the time series *x* (length *N*):

$$k = \frac{\frac{1}{N} \sum\_{i=1}^{N} (\boldsymbol{x}\_i - \boldsymbol{\mu}\_x)^4}{\sigma\_x^4},\tag{4}$$

The correlation sum is then calculated as

embedding vectors of the two different time series.

−200 0 200

> 0.5 1 1.5 2 2.5

EMG (

> time (s)

μV)

0 1 2 3

Healthy sub ject

time (s)

Recurrence plot

time (s)

**Figure 4.** EMG signals and recurrence plots of one healthy subject and one PD patient.

0.5 1 1.5 2 2.5

*<sup>C</sup>m*(*r*) = <sup>1</sup>

*N*<sup>2</sup> *m*

<sup>Θ</sup>(*s*) =

where *r* is the threshold distance. The correlation dimension is formally defined as

*r*→0

lim *Nm*→∞

Practically, *D*<sup>2</sup> is calculated as the slope of the regression curve in the log-log-representation. Recurrence rate [53] measures the percentage of recurring patterns in the EMG signal. It can be calculated from the embedding vector distances in (6) as a percentage of distances that are below of the threshold distance *r*. The binary image, that contains a value 1 in the cells (*i*, *j*) where *de*(*ui*, *uj*) *< r*, is called the recurrence plot. The recurrence plots of one healthy subject and one PD patient are illustrated in Figure 4. One can observe that the recurrence plot of the patient contains more cells with the value 1 (white cells) than the recurrence plot of the healthy subject. It means that the EMG signal of the patient contains more recurring patterns than the EMG signal of the healthy subject. In the cross-recurrence rate, the embedding vectors in (5) are formed for two time series and the Euclidean distances in (6) are evaluated between the

*D*2(*m*) = lim

*Nm* ∑ *i*,*j*=1

> 0, *s <* 0 1, *s* ≥ 0,

> > log *Cm*(*r*) log *r*

Θ(*r* − *de*(*ui*, *uj*)) (7)

Electromyography and Kinematic Measurements in Parkinson's Disease

Feature Extraction Methods for Studying Surface

0 1 2 3

PD patient

time (s)

Recurrence plot

time (s)

0.5 1 1.5 2 2.5

−200

0.5 1 1.5 2 2.5

0

200

. (8)

229

where *μx* is the mean and *σx* the standard deviation (SD) of the sample values. Parameter *k* is higher for more peaked signals.

The parameter *cr* was calculated as the width/height of the CR expansion. The width of the CR expansion was defined at the level of 50 crossings/second and the height as the maximum value of the CR expansion. Parameter *cr* is lower for more peaked signals.

#### *3.2.2. EMG parameters of nonlinear dynamics*

In [28, 29], we used parameters of nonlinear dynamics (correlation dimension, recurrence rate and cross-recurrence rate) for analyzing the EMG signal complexity and recurring EMG patterns. In nonlinear dynamics, the original time series (EMG signal) *x* is used to form embedding vectors *ui*

$$\boldsymbol{\mu}\_{i} = \begin{bmatrix} \boldsymbol{\pi}\_{i} \ \boldsymbol{\pi}\_{i+\lambda} \ \boldsymbol{\pi}\_{i+2\lambda} \ \dots \ \boldsymbol{\pi}\_{i+(m-1)\lambda} \end{bmatrix}\_{\boldsymbol{\nu}} \tag{5}$$

where *λ* is the delay parameter and *m* the embedding dimension [45]. The number of different embedding vectors is *Nm* = *Ne* − (*m* − 1)*λ* for each epoch (length *Ne*) of the time series *x*.

The correlation dimension [16] describes the complexity of the time series and it can be calculated from the embedding vectors as follows. First, the Euclidean distances between each pair of embedding vectors *ui* and *uj* in (5) are quantified as

$$d\_{\mathcal{E}}(\boldsymbol{\mu}\_{i\boldsymbol{\nu}}\boldsymbol{\mu}\_{j}) = \sqrt{\sum\_{k=0}^{m-1} |\boldsymbol{\chi}\_{i+k\boldsymbol{\lambda}} - \boldsymbol{\chi}\_{j+k\boldsymbol{\lambda}}|^{2}}.\tag{6}$$

The correlation sum is then calculated as

8 Will-be-set-by-IN-TECH

crossing rate variable of EMG *crr* and *crl* correlation dimension of EMG *D*2,r and *D*2,l recurrence rate of EMG %RECr and %RECl sample entropy of ACC SampEnr and SampEnl

coherence between EMG and ACC Cohr and Cohl

wavelet variable of EMG *W*max,r and *W*max,l

sample entropy of ACC SampEnr and SampEnl

Dynamic recurrence rate of EMG %RECr and %RECl cross-recurrence rate of EMG %RECr,l

> cross-wavelet variable of EMG *W*max,rl power of ACC *P*acc,r and *P*acc,l

**Table 1.** PD characteristic signal features and their notations. The subscripts r and l in the notations

In [28], we used two parameters (*k* and *cr*) for measuring the peakedness of EMG signals. The sample kurtosis was calculated as the fourth centered moment of the time series *x* (length *N*):

where *μx* is the mean and *σx* the standard deviation (SD) of the sample values. Parameter *k* is

The parameter *cr* was calculated as the width/height of the CR expansion. The width of the CR expansion was defined at the level of 50 crossings/second and the height as the maximum

In [28, 29], we used parameters of nonlinear dynamics (correlation dimension, recurrence rate and cross-recurrence rate) for analyzing the EMG signal complexity and recurring EMG patterns. In nonlinear dynamics, the original time series (EMG signal) *x* is used to form

where *λ* is the delay parameter and *m* the embedding dimension [45]. The number of different embedding vectors is *Nm* = *Ne* − (*m* − 1)*λ* for each epoch (length *Ne*) of the time series *x*. The correlation dimension [16] describes the complexity of the time series and it can be calculated from the embedding vectors as follows. First, the Euclidean distances between

> *m*−1 ∑ *k*=0

*ui* = [*xi xi*+*<sup>λ</sup> xi*+2*<sup>λ</sup>* ... *xi*+(*m*−1)*λ*], (5)


*<sup>i</sup>*=<sup>1</sup> (*xi* <sup>−</sup> *<sup>μ</sup>x*)<sup>4</sup> *σ*4 *x*

, (4)

*k* = 1 *<sup>N</sup>* <sup>∑</sup>*<sup>N</sup>*

value of the CR expansion. Parameter *cr* is lower for more peaked signals.

each pair of embedding vectors *ui* and *uj* in (5) are quantified as

*de*(*ui*, *uj*) =

stand for the side of the body.

228

higher for more peaked signals.

embedding vectors *ui*

*3.2.2. EMG parameters of nonlinear dynamics*

*3.2.1. Parameters of surface EMG signal morphology*

Computational Intelligence in Electromyography Analysis –

Task type Signal features Notations Isometric sample kurtosis of EMG *k*<sup>r</sup> and *k*<sup>l</sup>

$$\mathbb{C}^{m}(r) = \frac{1}{N\_{\overline{m}}^{2}} \sum\_{i,j=1}^{N\_{\overline{m}}} \Theta(r - d\_{\varepsilon}(u\_{i\prime} u\_{j})) \tag{7}$$

$$\Theta(s) = \begin{cases} 0, & s < 0 \\ 1, & s \ge 0, \end{cases}$$

where *r* is the threshold distance. The correlation dimension is formally defined as

$$D\_2(m) = \lim\_{r \to 0} \lim\_{N\_m \to \infty} \frac{\log C^m(r)}{\log r}.\tag{8}$$

Practically, *D*<sup>2</sup> is calculated as the slope of the regression curve in the log-log-representation.

Recurrence rate [53] measures the percentage of recurring patterns in the EMG signal. It can be calculated from the embedding vector distances in (6) as a percentage of distances that are below of the threshold distance *r*. The binary image, that contains a value 1 in the cells (*i*, *j*) where *de*(*ui*, *uj*) *< r*, is called the recurrence plot. The recurrence plots of one healthy subject and one PD patient are illustrated in Figure 4. One can observe that the recurrence plot of the patient contains more cells with the value 1 (white cells) than the recurrence plot of the healthy subject. It means that the EMG signal of the patient contains more recurring patterns than the EMG signal of the healthy subject. In the cross-recurrence rate, the embedding vectors in (5) are formed for two time series and the Euclidean distances in (6) are evaluated between the embedding vectors of the two different time series.

**Figure 4.** EMG signals and recurrence plots of one healthy subject and one PD patient.

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#### *3.2.3. Spectral-based parameters*

In spectral analysis, the aim is to present the signal in the frequency-domain by estimating its power spectral density (PSD). The PSD estimation can be based on a Fourier transform or wavelet transform or on parametric modeling. In [28, 29], the Fourier- and wavelet-based approaches were used for analyzing the EMG and acceleration signals of PD patients and healthy subjects.

The coherence was used in [28] for quantifying similarities in the power spectra of the EMG and acceleration signals. It was calculated from the PSDs of the EMG and acceleration signals (*Px*(*f*) and *Py*(*f*)) and from the cross-spectral density *Pxy*(*f*), which were estimated by using the Welch's averaged periodogram method [54]. The magnitude-squared coherence is defined as

$$\mathcal{C}\_{xy}(f) = \frac{|P\_{xy}(f)|^2}{P\_{\mathcal{X}}(f)P\_{\mathcal{Y}}(f)}\tag{9}$$

signal into a set of basis functions, which are obtained by scaling and shifting the wavelet function *ψ*(*t*). In continuous form, the wavelet transform of the signal *x*(*t*) is defined as

where *a* is the scale, *b* is the shift, and (·)<sup>∗</sup> denotes the complex conjugate operator. Different kinds of wavelet functions have been defined for analysis. For discrete signals one must use

If the wavelet transforms of two signals *x* and *y* are denoted with *Wx*(*a*, *b*) and *Wy*(*a*, *b*), the

In [29], the discrete Morlet wavelet was used for analysis as in many other EMG studies [10, 20, 40]. The scalograms (11) were calculated from the EMG signals of both sides of the body and the cross-scalogram (12) between the right and left side signals. The scalograms and cross-scalograms were scaled to present the percentage of energy for each wavelet coefficient as a function of time. The wavelet parameter *W*max was calculated as the maximum energy of all wavelet coefficients from both the scalograms and the cross-scalograms as a function of time. The wavelet cross-scalograms and parameters *W*max,rl are presented for one healthy subject and one PD patient in Figure 6. One can observe that in the wavelet cross-scalogram of the patient the energy is more spread into different wavelet coefficients than in the cross-scalogram of the healthy subject. Parameter *W*max,rl is lower for the patient.

Sample entropy is a parameter of nonlinear dynamics and it can be used for quantifying the regularity of acceleration signals in PD when compared to the healthy subjects. It was calculated in [28, 29] from the embedding vectors in (5) as described in [27]. In [29], the power of the acceleration signal was extracted from the dynamic acceleration recordings for

The aim in [28, 29] was to develop a method for discriminating between PD patients and healthy subjects on the basis of EMG and accelerations signal features. In total, the data from 42 PD patients and 59 healthy subjects were analyzed in [28] and the data from 49 PD patients

In [28, 29], there were many parameters that could capture essential information in the measured signals. These original signal features *pj* (*j* = 1, 2, ..., *Np*) (detailed in Table 1) were

*x*(*t*)*ψ*∗

*<sup>t</sup>* <sup>−</sup> *<sup>b</sup> a*

Electromyography and Kinematic Measurements in Parkinson's Disease

*dt*, (10)

231

*<sup>x</sup>* (*a*, *b*)|. (11)

Feature Extraction Methods for Studying Surface

*<sup>y</sup>* (*a*, *b*)|. (12)

 ∞ −∞

*Wx*(*a*, *<sup>b</sup>*) = <sup>1</sup>

*P<sup>W</sup>*

*P<sup>W</sup>*

wavelet cross-scalogram is defined as

*3.2.4.* **Acceleration signal features**

**3.3. Cluster analysis of subjects**

and 59 healthy subjects were analyzed in [29].

used to form feature vectors *zj* <sup>∈</sup> **<sup>R</sup>***Np* for each subject.

quantifying kinetic tremor and rigidity during movement.

√*a*

discrete wavelets. The magnitude-squared wavelet transform is called the scalogram

*<sup>x</sup>* (*a*, *b*) = |*Wx*(*a*, *b*)*W*<sup>∗</sup>

*xy*(*a*, *b*) = |*Wx*(*a*, *b*)*W*<sup>∗</sup>

and it gives values between 0 and 1. Variable Coh was calculated as the area of the coherence spectrum above a threshold value in the frequency range 0–50 Hz. The magnitude-squared coherence estimates of one healthy subject and one PD patient are presented in Figure 5. One can observe that the area of the coherence spectrum is larger for the PD patient than for the healthy subject.

**Figure 5.** EMG and acceleration signals and magnitude-squared coherence estimates of one healthy subject and one PD patient.

While in Fourier approach the basis functions in the spectral decomposition are global functions, in wavelet approach [1] the functions are local. Therefore, the wavelet-based methods can be more effective than the Fourier-based method in detecting time varying features in the spectrum [10]. The basic idea in the wavelet transform is to decompose the signal into a set of basis functions, which are obtained by scaling and shifting the wavelet function *ψ*(*t*). In continuous form, the wavelet transform of the signal *x*(*t*) is defined as

$$\mathcal{W}\_{\mathbf{x}}(a,b) = \frac{1}{\sqrt{a}} \int\_{-\infty}^{\infty} \mathbf{x}(t) \boldsymbol{\psi}^\* \left(\frac{t-b}{a}\right) dt. \tag{10}$$

where *a* is the scale, *b* is the shift, and (·)<sup>∗</sup> denotes the complex conjugate operator. Different kinds of wavelet functions have been defined for analysis. For discrete signals one must use discrete wavelets. The magnitude-squared wavelet transform is called the scalogram

$$P\_{\mathbf{x}}^{W}(a,b) = |\mathcal{W}\_{\mathbf{x}}(a,b)\mathcal{W}\_{\mathbf{x}}^{\*}(a,b)|. \tag{11}$$

If the wavelet transforms of two signals *x* and *y* are denoted with *Wx*(*a*, *b*) and *Wy*(*a*, *b*), the wavelet cross-scalogram is defined as

$$P\_{xy}^{W}(a,b) = |\mathcal{W}\_x(a,b)\mathcal{W}\_y^\*(a,b)|. \tag{12}$$

In [29], the discrete Morlet wavelet was used for analysis as in many other EMG studies [10, 20, 40]. The scalograms (11) were calculated from the EMG signals of both sides of the body and the cross-scalogram (12) between the right and left side signals. The scalograms and cross-scalograms were scaled to present the percentage of energy for each wavelet coefficient as a function of time. The wavelet parameter *W*max was calculated as the maximum energy of all wavelet coefficients from both the scalograms and the cross-scalograms as a function of time. The wavelet cross-scalograms and parameters *W*max,rl are presented for one healthy subject and one PD patient in Figure 6. One can observe that in the wavelet cross-scalogram of the patient the energy is more spread into different wavelet coefficients than in the cross-scalogram of the healthy subject. Parameter *W*max,rl is lower for the patient.

#### *3.2.4.* **Acceleration signal features**

10 Will-be-set-by-IN-TECH

In spectral analysis, the aim is to present the signal in the frequency-domain by estimating its power spectral density (PSD). The PSD estimation can be based on a Fourier transform or wavelet transform or on parametric modeling. In [28, 29], the Fourier- and wavelet-based approaches were used for analyzing the EMG and acceleration signals of PD patients and

The coherence was used in [28] for quantifying similarities in the power spectra of the EMG and acceleration signals. It was calculated from the PSDs of the EMG and acceleration signals (*Px*(*f*) and *Py*(*f*)) and from the cross-spectral density *Pxy*(*f*), which were estimated by using the Welch's averaged periodogram method [54]. The magnitude-squared coherence is defined

*Cxy*(*f*) = <sup>|</sup>*Pxy*(*f*)<sup>|</sup>

and it gives values between 0 and 1. Variable Coh was calculated as the area of the coherence spectrum above a threshold value in the frequency range 0–50 Hz. The magnitude-squared coherence estimates of one healthy subject and one PD patient are presented in Figure 5. One can observe that the area of the coherence spectrum is larger for the PD patient than for the

> −200 0 200

> > −0.1

0 0.1

0 0.5 1

**Figure 5.** EMG and acceleration signals and magnitude-squared coherence estimates of one healthy

While in Fourier approach the basis functions in the spectral decomposition are global functions, in wavelet approach [1] the functions are local. Therefore, the wavelet-based methods can be more effective than the Fourier-based method in detecting time varying features in the spectrum [10]. The basic idea in the wavelet transform is to decompose the

0 1 2 3 4

0 1 2 3 4

time (s)

EMG-ACC coherence

0 10 20 30 40 50

f (Hz)

Healthy sub ject

2

*Px*(*f*)*Py*(*f*) (9)

0 1 2 3 4

0 1 2 3 4

time (s)

EMG-ACC coherence

0 10 20 30 40 50

f (Hz)

PD patient

*3.2.3. Spectral-based parameters*

Computational Intelligence in Electromyography Analysis –

healthy subjects.

healthy subject.

−200 0 200

−0.1

0 0.1

0 0.5 1

subject and one PD patient.

arb.

EMG (

> ACC (g)

μV)

as

230

Sample entropy is a parameter of nonlinear dynamics and it can be used for quantifying the regularity of acceleration signals in PD when compared to the healthy subjects. It was calculated in [28, 29] from the embedding vectors in (5) as described in [27]. In [29], the power of the acceleration signal was extracted from the dynamic acceleration recordings for quantifying kinetic tremor and rigidity during movement.

#### **3.3. Cluster analysis of subjects**

The aim in [28, 29] was to develop a method for discriminating between PD patients and healthy subjects on the basis of EMG and accelerations signal features. In total, the data from 42 PD patients and 59 healthy subjects were analyzed in [28] and the data from 49 PD patients and 59 healthy subjects were analyzed in [29].

In [28, 29], there were many parameters that could capture essential information in the measured signals. These original signal features *pj* (*j* = 1, 2, ..., *Np*) (detailed in Table 1) were used to form feature vectors *zj* <sup>∈</sup> **<sup>R</sup>***Np* for each subject.

**Figure 6.** Right and left side EMG signals of one healthy subject and one PD patient. Wavelet cross-scalograms and *W*max,rl parameters for the healthy subject and the PD patient.

$$z\_{\mathbf{j}} = [p\_1 \ p\_2 \dots p\_{N\_p}]^T \tag{13}$$

during extension. The signal variables were normalized and the PC approach was applied separately for the flexion and extension phases of the movement as described in section 2.2. Cluster analysis was used in [28, 29] for grouping subjects with similar EMG and acceleration signal features into groups. This could be done by clustering the model weights (PCs) in the sum (1). An iterative k-means algorithm [47] was used for clustering the feature vectors of subjects in a two-dimensional feature space. In k-means algorithm, the only parameter given to the algorithm is the number of clusters. The algorithm begins by choosing initial estimates for each cluster center point. In each iteration step, it is determined to which cluster the feature vectors belong. The feature vector belongs to that cluster for which the squared Euclidean distance between the vector and the cluster center point in the two-dimensional feature space is minimized. The cluster center points are updated to be the mean of the feature vectors in each cluster in the two-dimensional feature space. The iteration continues until the sum of

233

Feature Extraction Methods for Studying Surface

Electromyography and Kinematic Measurements in Parkinson's Disease

The validation of the clustering results was performed by using the leave-one-out method. In the method, the eigenvectors and PCs are solved for each combination of *M* − 1 feature vectors, where *M* means the total number of feature vectors. That is, one feature vector is left out of the group each time the eigenvectors and PCs are computed. The clustering is then performed for each combination of *M* − 1 feature vectors, and in each case, it is tested to which cluster the feature vector that was left out belongs. In [28, 29], the correct ratings of clustering were defined as the percentage (mean±SD values) of healthy subjects that belong to the healthy subject cluster and the percentage of patients that belong to the patient clusters.

In [28], twelve features were extracted from the isometric EMG and acceleration signals of 59 healthy subjects and 42 PD patients. The normalized signal features (mean±SD values) for the healthy subject group and for the PD patient group are presented in Figure 7. The results show that the parameters SampEn, cr and *D*<sup>2</sup> seem to be lower and the parameters *k*, Coh and %REC higher for the patients than for the healthy subjects. That is, the EMGs of the patients tend to be less complex and contain more recurring patterns than the EMGs of the healthy subjects. The acceleration signals of the patients tend to be more regular and more coherent

The cluster analysis of subjects was performed in a two-dimensional feature space, that was spanned by the PC sum *θj*(2) + *θj*(5) and the first PC *θj*(1) by using the k-means algorithm. This PC sum was used, because it works better in discrimination than the single PCs. The results in Figure 7 show that 90 % of the healthy subjects belong to the cluster O1 and 76 % of the patients in two other clusters O2 and O3. Seven patients with severe motor symptoms are distinguished in O3. The ten patients in the healthy subject cluster O1 have only little or no tremor at all in their hands. The validation by using the leave-one-out method resulted in correct discrimination rates of 90 ± 1 % for the healthy subjects and 74 ± 6 % for the patients. In [29], ten features were extracted from the EMG and acceleration signals of 59 healthy subjects and 49 PD patients and used to form feature vectors for subjects. The normalized signal features (mean±SD values) for the healthy subject group and for the PD patient group

vector-to-center point distances summed over all clusters is minimized.

with the EMGs than the acceleration signals of the healthy subjects.

**3.4. Discrimination results**

The PC-based approach [19] was used in both studies for reducing the number signal features and for transforming the original possibly correlated parameters into uncorrelated parameters.

In [28], one feature vector was formed for each healthy subject, for each patient with medication on (MED on) and for 13 patients also with medication off (MED off, no medication 24 hours before the measurement) by using the twelve EMG and acceleration parameters (six parameters from each body side) that are detailed in Table 1. The original signal parameters were normalized (to zero mean and unit SD of all subjects) before applying the PC approach. The PC approach was applied once as described in section 2.2. In [29], two feature vectors were formed for each patient and for each healthy subject of the ten EMG and acceleration parameters that are detailed in Table 1. One of the feature vectors was formed by using the mean parameter values during flexion and the other by using the mean parameter values during extension. The signal variables were normalized and the PC approach was applied separately for the flexion and extension phases of the movement as described in section 2.2.

Cluster analysis was used in [28, 29] for grouping subjects with similar EMG and acceleration signal features into groups. This could be done by clustering the model weights (PCs) in the sum (1). An iterative k-means algorithm [47] was used for clustering the feature vectors of subjects in a two-dimensional feature space. In k-means algorithm, the only parameter given to the algorithm is the number of clusters. The algorithm begins by choosing initial estimates for each cluster center point. In each iteration step, it is determined to which cluster the feature vectors belong. The feature vector belongs to that cluster for which the squared Euclidean distance between the vector and the cluster center point in the two-dimensional feature space is minimized. The cluster center points are updated to be the mean of the feature vectors in each cluster in the two-dimensional feature space. The iteration continues until the sum of vector-to-center point distances summed over all clusters is minimized.

The validation of the clustering results was performed by using the leave-one-out method. In the method, the eigenvectors and PCs are solved for each combination of *M* − 1 feature vectors, where *M* means the total number of feature vectors. That is, one feature vector is left out of the group each time the eigenvectors and PCs are computed. The clustering is then performed for each combination of *M* − 1 feature vectors, and in each case, it is tested to which cluster the feature vector that was left out belongs. In [28, 29], the correct ratings of clustering were defined as the percentage (mean±SD values) of healthy subjects that belong to the healthy subject cluster and the percentage of patients that belong to the patient clusters.

#### **3.4. Discrimination results**

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**Figure 6.** Right and left side EMG signals of one healthy subject and one PD patient. Wavelet

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The PC-based approach [19] was used in both studies for reducing the number signal features and for transforming the original possibly correlated parameters into uncorrelated

In [28], one feature vector was formed for each healthy subject, for each patient with medication on (MED on) and for 13 patients also with medication off (MED off, no medication 24 hours before the measurement) by using the twelve EMG and acceleration parameters (six parameters from each body side) that are detailed in Table 1. The original signal parameters were normalized (to zero mean and unit SD of all subjects) before applying the PC approach. The PC approach was applied once as described in section 2.2. In [29], two feature vectors were formed for each patient and for each healthy subject of the ten EMG and acceleration parameters that are detailed in Table 1. One of the feature vectors was formed by using the mean parameter values during flexion and the other by using the mean parameter values

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In [28], twelve features were extracted from the isometric EMG and acceleration signals of 59 healthy subjects and 42 PD patients. The normalized signal features (mean±SD values) for the healthy subject group and for the PD patient group are presented in Figure 7. The results show that the parameters SampEn, cr and *D*<sup>2</sup> seem to be lower and the parameters *k*, Coh and %REC higher for the patients than for the healthy subjects. That is, the EMGs of the patients tend to be less complex and contain more recurring patterns than the EMGs of the healthy subjects. The acceleration signals of the patients tend to be more regular and more coherent with the EMGs than the acceleration signals of the healthy subjects.

The cluster analysis of subjects was performed in a two-dimensional feature space, that was spanned by the PC sum *θj*(2) + *θj*(5) and the first PC *θj*(1) by using the k-means algorithm. This PC sum was used, because it works better in discrimination than the single PCs. The results in Figure 7 show that 90 % of the healthy subjects belong to the cluster O1 and 76 % of the patients in two other clusters O2 and O3. Seven patients with severe motor symptoms are distinguished in O3. The ten patients in the healthy subject cluster O1 have only little or no tremor at all in their hands. The validation by using the leave-one-out method resulted in correct discrimination rates of 90 ± 1 % for the healthy subjects and 74 ± 6 % for the patients.

In [29], ten features were extracted from the EMG and acceleration signals of 59 healthy subjects and 49 PD patients and used to form feature vectors for subjects. The normalized signal features (mean±SD values) for the healthy subject group and for the PD patient group

**Figure 7.** Mean ± SD values of normalized signal features for the patient group (◦) and for the healthy subject group (+) (left). The cluster analysis of 42 PD patients (◦) and 59 healthy subjects (+) in the feature space (*θj*(2)+*θj*(5) with respect to *θj*(1)). The three clusters O1, O2 and O3.

in flexion and in extension are presented in Figure 8. The results show that parameters %REC and *P*acc tend to be higher and parameters SampEn and *W*max lower for patients than for healthy subjects both in flexion and in extension. That is, the EMGs of the patients tend to contain more recurring patterns than the EMGs of the healthy subjects and the EMG wavelet power tends to be more spread for patients. The acceleration signals of the patients tend to be of higher amplitude and more regular than the acceleration signals of the healthy subjects.

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healthy subjects (+) in the feature space (*θj*(2) with respect to *θj*(1)).

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**Figure 8.** Mean ± SD values of normalized signal features for the patient group (◦) and for the healthy subject group (+) in flexion and in extension (top). The cluster analysis of 49 PD patients (◦) and 59

during the isometric contraction of BB muscles (see section 3.1) and they were performed once for the healthy subjects and twice for the patients: with DBS on (stimulator was turned on) and with DBS off (stimulator was turned off). Ninth order Butterworth low-pass filter with 110 Hz cutoff was used for removing the DBS artifact from the EMG signals. The low-pass filtering was performed similarly for all subjects (patients and healthy subjects). The UPDRS -motor examination was performed for each patient with DBS on and with DBS off. The measured signals of one PD patient with DBS on and off are presented in Figure 9. One can observe that the EMG signal of the patient contains recurring EMG bursts and the acceleration signal

In [31], the PC-based approach was used for quantifying the effects of anti-parkinsonian medication on the basis of a set of EMG and acceleration signal features. In total, the measurement data from nine PD patients were analyzed. The subjects were measured in four different medication conditions: off-medication, and two and three and four hours after taking the medication. The isometric task (described in section 3.1) was analyzed. The UPDRS -motor examination was performed for each patient in each medication condition. The EMG and acceleration signals of one PD patient in each medication condition are presented in Figure

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The cluster analysis of subjects was performed in a two-dimensional feature space that was spanned by the second PC and the first PC by using the k-means algorithm. The results are presented in Figure 8. According to the results, the method can discriminate 80 ± 1 % of the patient extension movements from 87 ± 1 % of the extension movements of healthy subjects, and 73 ± 1 % of the patient flexion movements from 82 ± 1 % of the flexion movements of healthy subjects. The leave-one-out method was used for validation. The patients, that could not be discriminated from the healthy subjects, had mild motor symptoms of PD.
