A fuzzy clustering neural network architecture for ... - IEEE Xplore

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 11, NOVEMBER 2003

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A Fuzzy Clustering Neural Network Architecture for Multifunction Upper-Limb Prosthesis Bekir Karlik, M. Osman Tokhi*, Senior Member, IEEE, and Musa Alci

Abstract—Accurate and computationally efficient means of classifying surface myoelectric signals has been the subject of considerable research effort in recent years. The aim of this paper is to classify myoelectric signals using new fuzzy clustering neural network (NN) architectures to control multifunction prostheses. This paper presents a comparative study of the classification accuracy of myoelectric signals using multilayered perceptron NN using back-propagation, conic section function NN, and new fuzzy clustering NNs (FCNNs). The myoelectric signals considered are used in classifying six upper-limb movements: elbow flexion, elbow extension, wrist pronation and wrist supination, grasp, and resting. The results suggest that FCNN can generalize better than other NN algorithms and help the user learn better and faster. This method has the potential of being very efficient in real-time applications. Index Terms—Fuzzy clustering, myoelectric signal, neural network, pattern recognition, upper-limb prosthesis.

I. INTRODUCTION

I

N APPLICATIONS of prosthesis control, the identification of various myoelectric signals is used to control the movement of prostheses. The control strategy is based on generating a set of repeatable muscle contraction patterns and classifying these patterns in a suitable manner. In conventional methods, this strategy is slow and not reliable when the muscle contraction is different from the ordinary arm function. The information extracted from the myoelectric signal, represented in a feature vector, is used to minimize the control error. To achieve this, a feature set which maximally separates the desired output classes must be chosen. The need for a fast response of the prosthesis limits the processing time. The recognition of the signal characteristics can be carried out using a number of soft-computing approaches, such as neural networks (NNs) and fuzzy logic. For example; Chaiyaratana et al. have used two different types of radial basis function (RBF) NNs [1], Kely et al. [2], Ito et al. [3], and Karlik et al. [4] have used different structures of multilayered perceptron (MLP) NNs, Hudgins et al. have used Hopfield, adaptive resonance theory, and finite impulse response NN [5], and Englehart et al. [6], Del Boca and Park [7], and Seker [8] have used different types of fuzzy classification techniques. Manuscript received August 20, 2002; revised March 18, 2003. Asterisk indicates corresponding author. B. Karlik is with the Department of Computer Engineering, College of Information Technology, University of Bahrain, Kingdom of Bahrain. *M. O. Tokhi is with Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, U.K. (e-mail: [email protected]). M. Alci is with the Department of Electrical and Electronics Engineering, Engineering Faculty, Ege University, 35040 Bornova, Izmir, Turkey. Digital Object Identifier 10.1109/TBME.2003.818469

Most of the research that has been carried out involves utilization of MLP NNs with one hidden layer using the back-propagation algorithm. Very few researchers have used MLP NNs with two hidden layers [9]. Myoelectric signals can be drawn from various locations on a subject’s body. This is application dependent. For example, signals from flexor digitorium superficialis are used for classification of finger movements [10]. Signals from biceps and triceps branchii are used to describe arm movements [3], [5], [11]. The control signal can be derived from a single myoelectric channel [2], [4], [5], [9], or from multiple channels such as two [11], [12], four [3]; five [13], or eight channels [14]. With a single-channel myoelectric signal the NN structure may not be complex enough and high accuracy may not be achieved. However, with multichannel signals the positions of the electrodes become less critical and the classification accuracy increases [11]. Previous research is mostly concerned with the classification of arm movements. The experiments are usually carried out in two possible ways: loading of the subject’s arm with a weight [9] or allowing the subject to perform the movement naturally [5], [11]. The control schemes considered are almost entirely based on a discriminative approach to pattern recognition, where each pattern is described by a set of features. Feature sets can be obtained using various methods. For example, the parameters of a stochastic model such as an autoregressive (AR) model or autoregressive moving average (ARMA) model can be used as features set. A considerable amount of research has been carried out using AR models [1], [2], [4], [13], [15]–[19]. These are based upon the work reported by Graupe and Cline [20], which involves modeling myoelectric signals as ARMA models. Later research has shown that the use of an AR model is sufficient for modeling myoelectric signals. Graupe et al. have shown that a myoelectric signal epoch of 0.2–0.3 s can be modeled as a fourth-order AR model [15]. Different arm movements are considered in studying muscle contractions. AR parameters of myoelectric signals recorded from the muscles during these different movements are used as features to classify the signals with NN model. Various methods have been used to obtain the parameters of the AR model. One of the most common methods is the recursive least squares (RLS) or the sequential least squares (SLS) method [15]–[17], [19]. This method has been shown to be very reliable and has the capability to deal with noisy myoelectric signals. An extension of the RLS algorithm to accommodate multivariable AR models has been proposed by Doerschuk et al. [13], where parameters of the AR models from different channels are computed simultaneously. Other methods include

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the application of a discrete Hopfield network [2] and the partial autocorrelation (PARCOR) algorithm [4], [21]. Englehart and co-workers have used time-frequency based features and wavelet packet based feature sets [22], [23]. The classification problem may be divided into feature extraction, dimensionality reduction, and pattern recognition. Englehart et al. [23] have reported a solution based on a wavelet packet feature set. This has been shown to outperform other forms of signal representation except that reported by Karlik [24]. In the study presented in this paper the AR model parameters and the signal power are used as features with PARCOR methods for the feature sets. These feature sets are then clustered for different arm movements using a fuzzy C-means algorithm, and the clustering sets are used as input to an NN. The results of classification accuracy of this study are shown to be better than those reported by Englehart and co-workers. II. MYOELECTRIC SIGNALS FOR A HAND PROSTHESIS A myoelectric signal (MES) is generated by the action potentials propagating along the fibers of motor units of the muscle under contraction. This signal can be detected using invasive or noninvasive electrodes. Invasive electrodes are of wire or needle type and are able to detect the action potential generated by a single motor unit, with a reasonably high-amplitude power spectrum over a wide frequency range of up to 10 kHz [25]. In this work, bipolar surface electrodes consisting of two parallel silver bars, 1 cm apart, were used. The best location of the electrode is between the motor point and the tendon of insertion of the muscle, and the silver bars of the electrode should be perpendicular to these muscle fibers. As a differential amplifier is used, it is necessary to use a reference electrode; this electrode must have an area of about 4 cm and, to avoid interference with the measurements, should be located in a region with no muscles. The solution adopted was to place the electrode about the elbow of the subject. In order to reduce artefacts, which consist of low amplitudes, it is recommended to use active electrodes. To perform its function in the best way possible, the differential amplifier must have a high input impedance and high CMRR [26]. In this project a differential amplifier with a gain of 1000 was used. A low-pass filter with a cutoff frequency of 500 Hz was used to reduce high frequency noise and avoid signal aliasing due to sampling. Owing to the instability of signal components between 0 and 20 Hz, a high-pass filter with a cutoff frequency of 20 Hz was implemented. A notch filter of 50 Hz was used to remove the noise due to the mains power. It is important to point out that this filter must have a high quality factor not to compromise the signal, since the highest concentration of MES power is between 50 and 150 Hz. The extraction of features from a MES can be accomplished using various techniques described in Section I. AR modeling is used in this work. The AR model of a system is expressed as (1) where terns,

with representing the number of patis the value of the signal at , represents the order

of the model, represents the AR coefficients, and is white noise. There are several advantages associated with the use of an AR model in this application. It can be shown that a stationary time series can be represented using an AR model. Although an electromyogram (EMG) signal is not fully stationary, it is sufficiently stationary for each limb function considered, yielding AR parameters with adequately small ranges of variation over time to facilitate discrimination between limb functions. Each parameter of the AR model is a function of correlation between signals with delays, that is, with delays of up to sampling frequencies where is the model order. This implies that the lowest frequency represented in a model is dewhere is the sampling interval. Thus, if termined by a sampling frequency of 2 KHz is used the AR parameters of a fourth-order model would only contain information down to 500 Hz. However, for MESs, most of the signal power is in the low frequency range (below 300 Hz). The difference in the autocorrelation functions, in this case, is the largest between the first and fifth lags. This interval represents a frequency range of 100–500 Hz. It is this difference, which one is attempting to recognize in a signature discrimination system. For purposes of discrimination a sampling frequency of 500 Hz is used in this study. With a fourth-order model this implies that frequencies down to 125 Hz will be accounted for by the AR model parameters. In this study, the PARCOR algorithm is used to obtain the AR parameters [4], [24]. In the investigations presented in this paper EMG signals are obtained from a healthy person, and classified using the AR model parameters. These are in turn applied to an NN. Different movements, namely elbow extension, elbow flexion, wrist supination, wrist pronation, grasp and resting, are considered as classes and represented with four AR coefficients. Each movement is repeated six times and for each movement 4800 samples are collected. The 4800 samples are split into 12 segments of 400 samples each (80 ms). During NN training, a fuzzy controller is used to collect the 12-segment feature sets for each contraction. A Blackman type window function is used to perform windowing on each segment. These feature sets are then clustered for different arm movements using a fuzzy C-means algorithm, and the clustering sets are used as input to the NN. Moreover, for reasons of comparison, the feature sets are used as input to an ordinary MLP and a conic section NN. III. THE MULTI-LAYERED PERCEPTRON NEURAL NETWORK STRUCTURE AND TRAINING In this study a three-layered feed-forward NN is used and trained with the error back-propagation. Fig. 1 shows a general structure of the NN. The back propagation training with generalized delta learning rule is an iterative gradient algorithm designed to minimize the root mean square error between the actual output of a multilayered feed-forward NN and a desired output. Each layer is fully connected to the previous layer, and has no other connection. The cost function utilized is (2)

KARLIK et al.: FCNN ARCHITECTURE FOR MULTIFUNCTION UPPER-LIMB PROSTHESIS

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where is the th element of input vector is in the output layer (i.e., ) then set

. If neuron (9)

The error can be computed as (10) where .

is the th element of the desired response vector

C. Backward Computation of the NN by progressing Compute the local gradients backward layer by layer. For neuron in the output layer , the local gradient is given by (11) Fig. 1.

The general structure of MLP NNs.

For neuron in a hidden layer , the local gradient is given by

where represents the instantaneous cost function at iterais the error from output node at iteration and tion , represents the number of output nodes. The error from each output node is defined as

(12) The weight of the NN in layer can be adjusted according to the generalized delta rule as

(3) is the desired response of the output node at iterwhere is the output of the output node at iteration ation and Haykin gives a summary of the back-propagation algorithm as follows [27]. A. Initialization Set all the weights and threshold levels of the NN to small uniformly distributed random numbers. B. Forward Computation , with the Let a training example be denoted by applied to the input layer and the desired reinput vector presented to the output layer. The internal sponse vector for neuron in layer is given by activity level (4) is the signal from neuron in the previous layer where at iteration and is the weight of neuron in layer that is connected to neuron in layer at iteration . For the following holds (5) (6) is the threshold applied to neuron in layer . where Using a logistic function for the sigmoid nonlinearity, the output of neuron in layer is given as (7) If neuron is in the first hidden layer (i.e.,

) then set (8)

(13) where is the learning rate parameter and is the momentum constant. It may be noted here that a large value of the learning rate may lead to faster convergence but may also result in oscillation. In order to achieve faster convergence with minimum oscillation, a momentum term may be added to the basic weight updating equation. A value for the corresponding momentum correction factor between 0 and 1 may be chosen. In this study, the learning rate parameter was chosen as 0.95. The number of hidden nodes was determined via experimentation. The experimental results, as presented later, show that the optimum number of hidden nodes was seven with the highest classification accuracy of 97% for 2000 iterations. IV. CONIC SECTION FUNCTION NEURAL NETWORK The conic section function neural network (CSFNN) architecture was initially developed by Dorffner [28] and later improved by Yildirim and Marsland [29]. The CSFNN allows decision surfaces to be adapted between open boundaries as in MLP and closed ones as in RBF NNs, providing unification between RBF and MLP NNs. The propagation rule for CSFNN, which consists of RBF and MLP propagation rules, is derived using the analytical equation of a cone. Let be a point on the surface of a right circular cone with vertical angle in the range , be the vertex of the cone and represent a unit vector along the axis of the cone. Thus, a circular cone can be defined as (14) The intersection of a three-dimensional cone of vertex and with a plane forms a circle, a parabola, and opening angle a straight line in two-dimensional space by varying the opening angle. The angle changes with the height of the vertex. Straight line (hyperplane) and circle (hypersphere) represent the deci-

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Fig. 2. CSF NN architecture.

sion boarders for MLP and RBF NNs, respectively. Other types of decision boarders, such as ellipse and parabola can also be obtained, and these represent intermediate CSFs. The propagation rule of the CSFNN is given by

bership functions. The identified model can then be used to describe the behavior of the target system as well as for prediction and control purposes. The idea of fuzzy clustering is to divide the data into fuzzy partitions that overlap with one another. Therefore, the inclusion of data in a cluster is defined by a membership grade in . Formally, clustering an unlabeled data , where represents the number of data vectors and the dimension of each data vector, is the assignment of partition labels to the vectors in . -Partition membership values that of constitutes sets of matrix . can be conveniently arranged as a The problem of fuzzy clustering is to find the optimum membership matrix . The most widely used objective function for fuzzy clustering is the weighted within-groups sum of squared , which is used to define the following constrained errors optimization problem [30] (16) where

(15) represent connection weights between neurons of the where the center coinput and hidden layer in an MLP NN, and ordinates in an RBF NN, and are indexes associated with the neurons in the input and hidden layer, respectively. As can be seen, this equation consists of two major parts, analogous to the MLP and the RBF. The equation simply transforms into the propagation rule of an MLP NN (dot product; weighted sum) . The second part of the equation gives the Euwhen clidean distance between the inputs and the centers for an RBF NN. The structure of a CSFNN is illustrated in Fig. 2. The algorithm used for training the CSFNN improves the performance of back propagation. In this algorithm, the NN is initialized as an RBF and then is trained by back propagation after a certain number of centers have been obtained. The centers are determined using the orthogonal least squares (OLS) algorithm. The initially unbounded decision regions are made closer, for MLP initializations, through adaptation of the cone. In contrast, RBF initialization is achieved by starting the NN with an RBF, and then turning the hyperspherical decision regions into the open ones wherever appropriate. With RBF initialization, the weights and centers of all hidden units must be set. The weights are initialized using the weights derived from the training set. The centers are obtained using the OLS algorithm. The network is then trained using the back-propagation error algorithm and the weights and the opening angle parameter are updated until a minimum error goal or correct classification rate has been achieved. The gradient descent algorithm is used for updating the weights and the opening angle. Furthermore, in this study, training of the CSFNN was improved with an adaptive learning algorithm and inclusion of a momentum term in the back propagation algorithm. V. THE FUZZY CLUSTERING NEURAL NETWORK Structure identification of fuzzy systems is possible by constructing enough rules with appropriate input and output mem-

is the vector of (unknown) cluster cenis an inner product norm. is an ters, and positive definite matrix, which specifies the shape of the clusters. The matrix is commonly selected as the identity matrix, leading to Euclidean distance and, consequently, to spherical clusters. Fuzzy partitions are carried out using the fuzzy C-means (FCM) algorithm through an iterative optimization of [16] according to the following steps [31]: Step 1) Choose the number of clusters , weighting expo, iteration limit (iter), termination criterion nent , and norm for error . Step 2) Guess initial position of cluster centers: . , calculate Step 3) Iterate for (17) and

(18)

, THEN stop, and put NEXT . In this paper, a clustering-based approach is adopted for four AR parameters and their signal power used as input to the NN (see Fig. 3). In this paper, each movement is considered six times and each time 4800 samples are taken. Some of the data from the initial and final sections of the 4800 samples are removed to linearize the data. The 4800 samples are split into 12 segments IF

error


Fig. 3.

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Fuzzy neural classification of a multifunction prosthesis. TABLE I PARAMETER VALUES WITH CLUSTERS OF TWO FEATURES

of 400 samples. The 12-sample feature sets corresponding to each of the six different movements are clustered using the fuzzy C-means clustering algorithm before the NN training. Training is done with the back-propagation algorithm. The clustered data is applied as input to the NN, and can be clustered with different features, for example 2, 3, 4, and 6. Finally, the clustered data is classified using the NN. The values corresponding to clustering into two features for each movement are given in Table I, where clustered data of fuzzy cluster centers (from center 1 to center 6) belong to resting (R), wrist supination (WS), grasp (G), wrist pronation (WP), elbow extension (EE), and elbow flexion (EF), respectively. As noted in Table I, each Center 1 to Center 6 includes groups of two in each column (AR parameters and signal power). Thus, a total of 12 2 elements are obtained for the four AR parameters and for the signal power from the samples of data set. This is clustered into groups of two and Center 1 is found. The other centers are found similarly. A windows-based real-time monitoring software program was written using Pascal under Delphi, with the back-propagation algorithm in a supervised learning paradigm in which the generalized delta rule was used in adjusting the NN weights, see Fig. 4. The program is initiated by clicking on “Load file” upon which the EMG data is obtained from the person in real time. The iteration number and learning rate can be changed. The optimum learning rate and momentum coefficient were found as 2 and 0.1, respectively using different epochs, see Fig. 5. With clustering into two features the total number of feature sets is 2 6 5 where four AR parameters and the signal power of each movement are used. This corresponds to 1/6 the size of the real data, which is 12 6 5 for each movement. Table II shows the recognition rates with clusters of six features for the

Fig. 4.

The program monitor.

Fig. 5.

Optimum learning rate. TABLE II RECOGNITION RATES WITH CLUSTERS OF SIX FEATURES

six arm movements as obtained after 2000 iterations. The same data size (72 combinations for five nodes of input layer) was used for both training and testing. After the test, as noted, the recognition rates vary between 95% and 100%, with average recognition accuracy of 98%. Table III describes the recognition rates with clustering into two features for the same six movements as obtained after 2000 iterations. As noted the recognition rates vary between 96% and 100%, with an average recognition accuracy of about 99%. It follows from these results that the recognition rate is reduced with a reduction in the clustering rate. VI. RESULTS Three different training and test sets were used in this investigation. First, all samples were used for training and testing using MLP, CSFNN, and FCNN. The corresponding results for the

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TABLE III RECOGNITION RATES WITH CLUSTERS OF TWO FEATURES

Fig. 6. Classification results of the four methods.

generalized case in terms of different convergence rates were 97% for MLP, 88% for CSFNN and 98% for FCNN with clusters of two features after 2000 iterations. Fig. 6 shows the classification results of the three methods and two different clustering types used in this study. As noted, with all the three methods, the classification rate decreases as the number of iterations increases. It is noted in the results above that the FCNN converges to a determined error goal faster than both the MLP and CSFNN. Moreover, in most cases, compared to other NNs, more accurate classification rates (of 98.3%) are obtained with the FCNN. This result is significantly better than those previously reported; Karlik found 96.1% classification rate [24], and Englehart et al. found 93.7% classification rate as the best results of their study [22]. VII. CONCLUSION A strategy for the control of a multifunction myoelectric prosthesis for upper limbs has been developed and presented. Two limitations of current multifunction myoelectric control systems are: 1) the limited information content in the available control signals and 2) the large amount of data required for the classification of the desired function. A comparative assessment of the performance of FCNN with MLP NN and CSFNN show that more reliable results are obtained with the FCNN for the classification of EMG signals to control multifunction prostheses. MLP NNs are still able to generalize with good recognition accuracy. However, they take longer to train. The aim in developing FCNN was to achieve more optimum results with relatively few signal features. It has been demonstrated that the training time of the FCNN was ap-

proximately half the time required by the MLP NN. CSFNN is also very fast, but its recognition accuracy is not as good as that achieved with the MLP NN and FCNN. It will be worthwhile, in future studies, to use cepstral coefficient as a feature set. Previous studies have reported 83.7% classification rate using the cepstral coefficient method when classifying ten distinct gestures with four channels of recorded data. Englehart et al. attempted to classify EMG signals using various time-frequency based representations with dimensionality reduction [22]. In their experiments, they achieved a maximum classification accuracy of 93.7% using the wavelet-based feature set. With a PARCOR algorithm to estimate the AR parameters, on the other hand, 96.1% classification rate has been achieved using MLP. Other estimation methods of AR have resulted in classification rates of 78.7%. Hudgins et al. have implemented their pattern recognition based myoelectric control system as a controller embedded on a digital signal processing device [32]. This controller has shown early success in clinical trials. The strategy proposed in this paper can be easily realized into such control software; it is anticipated that the resulting improvement in accuracy will enhance the functionality of prosthetic control. Moreover, the results of this work can be easily generalized to other procedures that require quantitative and decision-based analyses. Furthermore, FCNN can be chosen for implementation on a microprocessor in prosthesis devices. In the future, it will be possible that combined movements, such as hand close/wrist flexion, be classified. These would enable simultaneous control of devices to enhance the anthropomorphism of control, offering benefits of functionality and dynamic cosmoses. REFERENCES [1] N. Chaiyaratana, A. M. Zalzala, and D. Datta, “Myoelectric signals pattern recognition for functional operation of upper-limb prosthesis,” in Proc. ECDVRAT, Maidenhead, U.K., 1996, pp. 151–160. [2] M. Kelly, P. A. Parker, and R. N. Scott, “The application of neural networks to myoelectric signal analysis: A preliminary study,” IEEE Trans. Biomed. Eng., vol. 37, pp. 221–227, Mar. 1990. [3] K. Ito, T. Tsuji, A. Kato, and M. Ito, “Limb-function discrimination using EMG signals by neural network and application to prosthetic forearm control,” in Proc. IEEE Int. Joint Conf. Neural Networks, Singapore, 1991, pp. 1214–1219. [4] B. Karlik, H. Pastaci, and M. Korurek, “Myoelectric neural networks signal analysis,” in Proc. 7th Mediterranean Electrotech. Conf., vol. 1, Antalya, Turkey, 1994, pp. 262–264. [5] B. Hudgins, P. A. Parker, and R. N. Scott, “A new strategy for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 40, pp. 82–94, Jan. 1993. [6] K. Englehart, B. Hudgins, M. Stevenson, and P. A. Parker, “A dynamic feed forward neural network for subset classification of myoelectric signal patterns,” presented at the 19th Annu. Int. Conf. IEEE EMBS/CMBEC 21, Montreal, QC, Canada, 1995. [7] A. Del Boca and D. C. Park, “Myoelectric signal recognition using fuzzy clustering and artificial neural networks in real time,” in Proc. IEEE Int. Conf. Neural Networks, vol. 5, Orlando, FL, 1994, pp. 3098–3103. [8] H. Seker, “Classification of EMG signals using fuzzy classifiers,” masters thesis, Istanbul Tech. Univ., Istanbul, Turkey, 1995. [9] J. D. Costa and R. E. Gander, “MES classification using artificial neural networks and chaos theory,” in Proc. Int. Joint Conf. Neural Networks, vol. 3, Nagoya, Japan, 1993, pp. 2243–2246. [10] A. Hiraiwa, K. Shimohara, and Y. Tokunaga, “EMG patterns analysis and classification by neural network,” in Proc. IEEE Int. Conf. Syst. Man Cybern., vol. 3, Cambridge, MA, 1989, pp. 1113–1115. [11] U. Kuruganti, B. Hudgins, and R. N. Scott, “Two-channel enhancement of a multifunction controls system,” IEEE Trans. Biomed. Eng., vol. 42, pp. 109–111, Jan. 1995.


[12] E. C. Yeh, W. P. Chung, R. C. Chan, and C. C. Tseng, “Development of neural networks controller for below-elbow prosthesis using single-chip microcontroller,” Biomed. Eng. Appl. Bas. Commun., vol. 5, no. 3, pp. 340–346, 1993. [13] P. C. Doerschuk, D. E. Gustafson, and A. S. Willsky, “Upper extremity limb function discrimination using EMG signal analysis,” IEEE Trans. Biomed. Eng., vol. BME-30, pp. 18–29, Jan. 1983. [14] L. Eriksson, F. Sebelius, and C. Balkenius, “Neural control of a virtual prosthesis,” presented at the ICANN 98, Perspectives in Neural Computing, Skövde, Sweden, 1998. [15] D. Graupe, J. Salahi, and D. Zhang, “Stochastic analysis of myoelectric temporal signatures for multifunction single-site activation of prostheses and orthoses,” J. Biomed. Eng., vol. 7, no. 1, pp. 18–29, 1985. [16] T. Kiryu, C. J. De Luca, and Y. Saitoh, “AR modeling of myoelectric interference signals during a ramp contraction,” IEEE Trans. Biomed. Eng., vol. 41, pp. 1031–1038, Nov. 1994. [17] A. Latwesen and P. E. Patterson, “Identification of lower arm motions using the EMG signals of shoulder muscles,” Med. Eng. Phys., vol. 16, no. 2, pp. 113–121, 1994. [18] R. Merletti and L. R. Lo Conte, “Advances in processing of surface myoelectric signals: Part 1,” Med. Biol. Eng. Comput., vol. 33, pp. 362–372, 1995. [19] M. Zardoshti-Kermani, B. C. Wheeler, K. Badie, and R. M. Hashemi, “EMG features selection for movement control of a cybernetic arm,” Cybern. Syst. Int. J., vol. 26, no. 2, pp. 189–210, 1995. [20] D. Graupe and K. W. Cline, “Functional separation of EMG signals via ARMA identification methods for prosthesis control purposes,” IEEE Trans. Syst., Man, Cybern., vol. 5, no. 2, pp. 252–259, 1975. [21] B. Karlik and Y. Ozbay, “An improved study for multifunctional myoelectric control,” in Proc. ISEK’96, Enschede, The Netherlands, Oct. 1996, pp. 164–165. [22] K. Englehart, B. Hudgins, P. A. Parker, and M. Stevenson, “Classification of the myoelectric signal using time-frequency based representations,” Med. Eng. Phys. (Special Issue: Intell. Data Anal. Electromyogr. Electroneurogr.), vol. 21, pp. 431–438, 1999. [23] K. Englehart, B. Hudgins, and P. A. Parker, “A wavelet based continuous classification scheme for multifunction myoelectric control,” IEEE Trans. Biomed. Eng., vol. 48, pp. 302–311, Mar. 2001. [24] B. Karlik, “Differentiating type of muscle movement via AR modeling and neural networks classification of the EMG,” ELEKTRIK (Turkish J. Elect. Eng. Comput.), vol. 7, no. 1–3, pp. 45–52, 1999. [25] J. G. Webster, Medical Instrumentation: Application and Design, 3rd ed. New York: Wiley, 1997. [26] (1996) A Discussion on Surface Electromyography: Detection and Recording. Delsys Inc. [Online]. Available: http://www.delsys.com/emg_articles/EMG.shtml [27] S. Haykin, Neural Networks: A Comprehensive Foundation. New York: Macmillan, 1994. [28] G. Dorffner, “Unified framework for MLP’s and RBFNs: Introducing conic section function networks,” Cybern. Syst., vol. 25, pp. 511–554, 1994. [29] T. Yildirim and J. S. Marsland, “Improved back propagation training algorithm using conic section functions,” presented at the IEEE ICNN’97, Houston, TX, June 1997.

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[30] J. C. Bezdek, Pattern Recognition With Fuzzy Objective Function Algorithms. New York: Plenum, 1981. [31] M. R. Emami, I. B. Turksen, and A. A. Goldenberg, “An improved fuzzy modeling algorithm, Part II: System identification,” in Proc. NAFIPS, 1996, pp. 294–298. [32] B. Hudgins, K. Englehart, P. A. Parker, and R. N. Scott, “A microprocessor-based multifunction myoelectric control system,” presented at the 23rd Canadian Medical and Biological Engineering Society Conf., Toronto, ON, Canada, 1997.

Bekir Karlik received the B.E., M.E., and Ph.D. degrees from Yildiz Technical University, Istanbul, Turkey, in 1988, 1991, and 1994, respectively. He is currently an Associate Professor in the Department of Computer Engineering, University of Bahrain, Bahrain. His research interests include intelligent control systems and robotics, biomedical signals and image processing, and neural-fuzzy systems. He is an editor of Mathematical and Computational Applications.

M. Osman Tokhi (M’89–SM’97) received the B.Sc. degree in electrical engineering from Kabul University, Kabul, Afghanistan, in 1978 and the Ph.D. degree from Heriot-Watt University, Edinburgh, U.K., in 1988. He has worked as Lecturer and Senior Lecturer in Kabul University, Glasgow College of Technology (Glasgow, U.K.), and the University of Sheffield (Sheffield, U.K.) and as Sound Engineer in industry. He is currently employed as Reader in the Department of Automatic Control and Systems Engineering, The University of Sheffield. His research interests include active noise and vibration control, biomedical signal processing and control, real-time signal processing and control, and soft-computing and adaptive/intelligent control.

Musa Alci received the B.Sc. and M.Sc. degrees in engineering from the Technical University of Istanbul, Istanbul, Turkey. He received the Ph.D. degree from Sakarya University, Sakarya, Turkey, in 1999. Since 2000, he has been a faculty member with Ege University, Bornova, Turkey, where he is Assistant Professor of Electrical and Electronics Engineering. His research interests include fuzzy logic, neural networks, control systems, and system identification.