Implementation of Artifact Removal Algorithms in Gait Signals for Diagnosis of Parkinson Disease

Moore et al. [14] utilized a portable/mobile device in their study to monitor Freezing of Gait (FOG) by using frequency features pertaining to vertical leg motion for FOG as commonly seen in advanced PD patients. They have used this device [15], which they developed to determine stride length in their previous studies, to detect FOG in 11 patients with advanced PD. Vertical linear acceleration of the left leg was procured using an ankle-mounted 100 Hz frequency sensor array wirelessly transmitting data to a pocket PC. 89% success rate was achieved in detecting FOG through this study. A similar study for FOG detection was carried out by Tripoliti et al. [16]. Signals received from wearable sensors (six accelerometers and two gyroscopes) placed on the patient's body were utilized to detect freezing of gait (FOG) in PD patients. Four classification algorithms were tested in the study by using signals recorded from five healthy individuals, five patients with FOG symptoms, and six patients with PD but without FOG symptoms (Naïve Bayes, Random Forests, Decision Trees, and Random Tree). In this study, they were able to detect incidents of FOG with 96.11% accuracy using the Random Forests classification algorithm. In the study conducted by Camps et al. [17], the deep learning method was utilized to detect FOG episodes in PD patients. This model is trained up via a new spectral data representation strategy that takes the information from both previous and existing signal windows into account. In this study, the evaluation was conducted using the data collected via an inertial measurement unit placed on the waist of 21 PD patients who displayed FOG episodes. The presented deep learning method is feed-forward 1D-ConvNet and has shown a performance of about 90%.

The VGRF data obtained from Physionet, which was also used in this study, was utilized to conduct various studies for the purpose of PD diagnosis. Alkhatib [18] suggested an autoregressive model, which is a statistical method, in one of their studies to analyze the VGRF time series data, and in another one, they used the K-nearest neighbors (KNN) method, which is a supervised machine learning method. In their study, they used the data from 18 healthy individuals and 29 people with PD. That being said, in this study, only the sensor data in the inner arch of the foot sole was utilized for each foot by discarding other important sensory information.

Samà et al. [19] proposed in their study a machine learning method to analyze the signals provided by a three-axis accelerometer that is placed on the waist of PD patients for the detection of bradykinesia, which is the most important symptom of patients with PD and presents itself as the slowness of motion. In this method, Support Vector Machines were used to determine the sections of the signals corresponding with gait. The epsilon-Support Vector Regression model was then used to assess bradykinetic gait attacks and predict the degree of bradykinesia using the frequency content of the steps. The method was tested on 12 persons with PD, and the frequency content of the steps resulted in an accuracy of better than 90% in dividing the bradykinesia in two.

After approximation coefficients and detail coefficients were obtained by applying wavelet transformation (WT) to VGRF signals by Lee and Lim [20], a classification was made with Neural Network with Weighted Fuzzy Membership functions (NEWFM). In this study, signals belonging to 93 PD and 73 control individuals were classified with the highest success performance of 77.33%. In another study by Zhang et al. [7], a classification was made with Sparse Representation theory and SVM-based classifiers using the Fourier Transformation coefficients obtained in these VGRF signals to classify patients and healthy individuals. Classification accuracies with a percentage of respectively 83.44% and 81.53% were obtained using Rare Approach and SVM classifiers. In a study conducted by Dairi [21], features obtained by applying short-time Fourier transform (STFT) to the same data set were reduced by the feature discriminant ratio (FDR) method and classified with SVM. It is stated that the proposed approach categorizes the signals of 93 people with PD and 73 healthy individuals control with great success. In another study conducted by Zeng et al. [22], a method based on deterministic learning theory was proposed to make gait analysis from the same VGRF data and diagnose people with PD and healthy control individuals. Features were extracted from differences in the signals obtained for each foot via the wearable sensors, and the subjects whose gait dynamics were registered were classified using the radial basis function (RBF) neural network. In this study, when the data of 93 people with PD and 73 healthy people were classified, success performance of 96.39% was obtained.

In a study conducted by Khorasani and Daliri [23], a data set consisting of 16 healthy and 15 sick people was used. Hidden Markov Model (HMM) with Gaussian Mixtures was used to detect PD, and 90.32% success performance was achieved. In the study conducted by Wu and Krishnan [24] on the same data set, the same performance results were obtained using the least-squares support vector machine (LS-SVM) classifier.

In the study of Perumal and Sankar [1], the effect of using gait and trembling features for early detection and monitoring of PD was investigated. Using VGRF data obtained from wearable sensors, various features were derived, and statistical analysis and machine learning techniques were utilized to find out the most distinguishing features among subjects with PD and healthy subjects. Accordingly, it was observed that a number of gait features such as stride distance, posture and phases of oscillation, heel and normalized heel forces provide better performance (feature separation) than others. 86.9% accuracy rate on average was achieved in the classification between a PD patient and a healthy control subject.

In the study of Abdulhay et al. [4], a new approach was proposed to diagnose PD using gait analysis made up of gait cycles which can be divided into several phases and periods to determine normative and abnormal gait. First of all, raw VGRF data obtained from the Physionet database were cleaned from noise using Chebyshev type II high pass filter. By using peak detection and pulse time measurement techniques, the filtered data was used to extract various gait features, and different temporal characteristics such as posture, oscillation, and stride time were obtained. An accuracy of 92.7% on average was obtained in the diagnosis of PD from gait analysis, and tremor analysis was used to determine the severity of PD.

In the method section, noise removal methods from walking signals, LBP transformation for feature extraction, and the obtained statistical features are presented.

4.1 One dimensional local binary Patterns (1D-LBP)

In the study, 1D-LBP was utilized as a feature extraction method to capture important information for the diagnosis of PD through the gait signals from individuals. The 1D-LBP method has been developed to be used in different application areas in data processing for signals with a dimensional sequence in the form of a time series [31-33]. Binary codes are obtained by making binary comparisons with each value determined as the center value on the signal and the neighboring values. This process is repeated throughout the signal. The values obtained from the decimal equivalents of these binary codes make up the 1D-LBP signal [31].

The mathematical formula of the binary comparison is as follows. P_i; ith neighbors, P_c; indicates the center value. The 1D-LBP method is described step by step on a section of the sampling signal. Figure 3 displays the central points and neighborhoods received from the signal to apply the 1D-LBPmethod.

$\begin{aligned}

&a=P c-P_{i} \\

&L B P(x)=\sum_{i=1}^{P} f(a) 2^{i-1} \quad f=\left\{\begin{array}{l}

1, a \geq 0 \\

0, a<0

\end{array}\right.

\end{aligned}$     (1)

In the second stage, binary values are obtained by comparing the P = {P1, P2, P3, P4, P5, P6, P7, P8} values specified in Figure 4 (B) with the Pc value. It takes the value one (1) if the adjacent P_i value is greater than or equal to the central value; otherwise, it takes the value zero (0) (Figure 3 (C)).The steps required to calculate the 1D-LBP code are as follows; In the first stage, the 1D-LBP operator in this given signal is obtained as a result of binary comparisons between the center value and neighboring values. For each value on the signal, a total number of P neighboring values are selected before and after. P / 2 neighbor as before and P / 2 as after are taken as values. In this study, eight neighboring points were determined with P=8. When each point is taken as the center value (Pc), it takes place before the center value (Pc), at (P1, P2, P3, P4) and then (P5, P6, P7, P8) (Figure 3 (B)).

In the third stage, the binary LBP codes take place in center values in comparisons. These binary codes represent the local structure information around the PC points, to which a decimal value is given. Then, this obtained binary string is converted to a decimal value (Figure 3 (D)).

In the fourth stage, the above steps are performed for all values on the individual signal. With this method, 1D-LBP signal is obtained from the signals in the range between 0-255. In other words, the 1D-LBP signal consists of values in the range between 0-255. The frequency of each value obtained is the expressed version of a pattern. The histogram machine learning of 1D-LBP signals is used as a feature vector for methods.

4.2 Spatial filter methods

Common Average Reference (CAR), Median Common Average Reference (MCAR), and Weighted Common Average Reference (WCAR) filter and methods, which are commonly used, are described in this section.

4.2.1 Common average reference (CAR) filter method

In the CAR filtering method, it is assumed that the cleaned noise si (t) signal of the observed zi (t) signal in the i channel at the time of t and the noise generated by the signals measured from other channels is the mixture of n (t) of the term.

$z_{i}(t)=s_{i}(t)+n(t)$    (2)

3.png

Figure 3. Calculating 1D-LBP code through the signals of a sample raw signal

Here i=1,2,3, ..K refers to channels. t=1,2,3,4.. L indicates the length of the signal. In total, there is K number of channels and L number of sample values in the signal. In the CAR algorithm, the term noise can be estimated by calculating the average of all channels, assuming that common noise contributes similarly in all channels:

$\hat{n}(t)=\frac{1}{K} \sum_{i=1}^{K} z_{i}(t)$     (3)

Here $\hat{n}(t)$  indicates the average of all channels for an estimate of noise. Accordingly, by removing this average noise term from each channel, a clean signal is obtained for each channel.

$\hat{s}_{i}(t)=z_{i}(t)-\hat{n}(t)$     (4)

The main disadvantage of the CAR method is that any channel-specific noise propagates to all channels.

4.2.2 Median common average reference (MCAR) filter method

In Median CAR, the median of all channels is used to estimate noise at each time point:

$\hat{n}(t)=z_{i}(t)\left(\frac{K+1}{2}\right) \text { if } K \text { is odd }$     (5)

$\hat{n}(t)=\left(z_{i}(t)_{\frac{K}{2}}+z_{i}(t)_{\frac{K}{2}+1}\right) / 2 \text { if } K \text { is even }$      (6)

Here, K shows the total number of channels. Median is more sensitive to outliers in data than its average parameter [34].

4.2.3 Weighted common average reference (WCAR) filter method

The major drawback of the standard CAR is that it assumes that common noise spreads similarly in the channels. Z_i(t) signal registered in the WCAR method, the clean s_i(t) signal, and noise term are modeled with an autoregressive (AR) structure between n(t).

$z_{i}(t)=s_{i}(t)+w_{i}(t)^{T} n(t)$    (7)

Here n(t)=[n(t)n(t-1)n(t-2)…n(t-M+1)]^T indicates the noise vector. M is the window size on the signal. W(t) is the weight vector indicating the weights of the noise term and is specified as w(t)=[w₁w₂w₃w₄….w_M]^T. In the WCAR method, it is assumed that the common noise is distributed in channels with different amplitudes and polarities. Kalman filter was applied to find weight vectors for each channel. Then in order to estimate weights, z_i(t) signals are expressed in a discrete-time Markovian state-space model [35].

$z_{i}(t)=s_{i}(t)+w_{i}(t)^{T} n(t)$     (8)

$w_{i}(t+1)=\alpha w_{i}(t)+\delta_{i}(t)$     (9)

Here α is a fixed number. δ_i(t) is the noise term with normal distribution for each channel. The covariance of this term $V_{i}=E\left(\delta_{i} \delta_{i}^{T}\right)$ and its average are considered to be zero. On measured signals, s_i(t) has an average of zero, and its variance is considered as $q=E\left(s_{i}^{2}\right)$. Based on the Kalman filter frame, weights w_i(t) are estimated in two stages [34].

1) Status update depending on the previous situation:

$\widehat{w}_{i}^{-}(t)=\alpha \widehat{w}_{i}(t-1)$    (10)

$P_{i}^{-}(t)=\alpha P_{i}^{-}(t-1)+V_{i}(t)$      (11)

Here $P_{i}^{-}(t)$ is the covariance matrix of the estimated error. Here α is the state transition parameter. Updates can be performed with different values.

$X_{1}=\left[w_{1}(1) \ldots w_{i}(L-1)\right]$     (12)

$X_{2}=\left[w_{2}(2) \ldots w_{i}(L)\right]$     (13)

where, L is the sample number in each i channel, the alpha parameter corresponding to each channel can be defined as follows:

$\alpha_{i}=X_{2} X_{1}^{T}\left(X_{1} X_{2}^{T}\right)^{-1}$     (14)

2) Change of situation based on new measurement:

$\widehat{w}_{i}(t)=w_{i}^{-}(t)+K_{i}(t)\left[z_{i}(t)-n^{T}(t) \widehat{w}_{i}^{-}(t)\right]$    (15)

$P_{i}(t)=\left[I-K_{i}(t) n^{T}(t)\right] P_{i}^{-}$     (16)

$K_{i}(t)=P_{i}^{-}(t) n(t)\left[n^{T}(t) P_{i}^{-}(t) n^{T}(t)+q\right]^{-1}$     (17)

Here $\widehat{w}_{i}(t) \text { and } P_{i}(t)$ specify the covariance matrices of the updated status and error, respectively. The K_i(t) is the term Kalman gain. It adjusts the contribution of new observation values to update the status parameter. The Kalman gain can be repeated according to the equation above. For more detailed information about WCAR, the study conducted by Khorasani et al. [35] can be examined.

4.3 Proposed method

In this study, a completely different approach, as opposed to other studies, was proposed to detect PD from walking signals. The proposed method is a statistical approach that uses patterns obtained as a result of comparisons between the neighbors of each value on multichannel recorded signals. The block diagram of the proposed approach is given in Figure 4.

4.png

Figure 4. The proposed system for PD diagnosis

Table 3. Statistical features from the signals [30]

Block 1: Indicates walking signals recorded from raw multichannel patients and healthy individuals. These are signals measured from a total of 18 channels.

Block 2: Noises coming directly from the recorded multichannel signals were cleared by CAR, MCAR, and WCAR methods. These three different methods were applied to the signals separately.

Block 3: 1D-LBP conversion was applied to the signals obtained from all channels. This method provides distinctive patterns for the diagnosis of PD.

Block 4: After the 1D-LBP signals were obtained, histograms of these signals were procured in each channel.

Block 5: Statistical features were extracted from the histograms of 1D-LBP signals. Twelve different statistical features were gathered. Statistical features extracted from histograms are presented in Table 3.

Block 6: It is the classification stage. LR (Logistic Regression), RF (Random Forest), and Knn (K-nearest neighbor) machine learning methods were used. The classification process was carried out according to the tenfold cross validity test with the WEKA software.

Block 7: is the decision phase. It indicates whether the signal belongs to a healthy or sick person. Common Average Reference (CAR), Median Common Average Reference (MCAR), and Weighted Common Average Reference (WCAR) filter and methods, which are commonly used, are described in this section.

4.4 Performance criteria

The accuracy rate belonging to the most popular and simple model was examined to determine how successful the proposed model was. This ratio was defined as the ratio of the number of correctly classified (TP + TN) samples to the total number of samples (TP + TN + FP + FN) [35]. Sometimes, on the contrary, the performance rate of the model is found by determining the error rate, which is expressed as the ratio of the number of incorrectly classified samples to the total number of samples [36]. Accuracy, precision, and f-criterion criteria were utilized in this study.

$\text { Accuracy }=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$     (18)

$\text { Error rate }=\frac{F P+F N}{T P+T N+F P+F N}$     (19)

$\text { Precision }=\mathrm{TN} /(\mathrm{TN}+\mathrm{FP})$      (20)

$\text { Recall }=\mathrm{TP} /(\mathrm{TP}+\mathrm{FN})$     (21)

$\begin{gathered}

\mathrm{F}-\text { Measure }=(2 x \text { Recall } * \text { Precision }) /(\text { Recall } \\

+\text { Precision })

\end{gathered}$      (22)

In these equations, T, F, P, and N denote True, False, Positive, and Negative, respectively. For example, TP is the number of correctly classified positive samples; FN indicates the number of incorrectly classified negative samples.

In this study, a new approach was proposed to differentiate individuals with PD from healthy individuals through gait signals. Gait and tremor signals are widely used in the diagnosis of PD. Gait signals are generally measured in a multichannel way. While the signals are measured in one channel, other channels may encounter a noise effect. Therefore, CAR, MCAR, and WCAR methods were applied to the gait signals to remove possible noises in the signals. After applying the LBP conversion, statistical features were extracted from the formed clean signals. These feature groups were classified by classification algorithms such as Knn, LR, and RF. When the results are considered, it was determined that the WCAR method, which is an adaptive method, clears noise best. As the classification method, the best classifier was observed as the Knn method. The best success rate was found as 92.96%.

The study also examined signals on which foot was effective in diagnosing PD. According to the data set used, it was observed that the signals on the left foot provide better distinctive features in the diagnosis of PD. In addition, it was determined which sensors under the feet are effective in diagnosing PD.

In order to demonstrate the effectiveness of the proposed method, the classification process was performed by applying LBP transformation without applying noise-cleaning algorithms to the gait signals and by extracting statistical features. When the results were analyzed, it was determined that noise-cleaning methods increased overall success.