Fuzzy clustering algorithms are helpful when there exists a dataset with subgroupings of points having indistinct boundaries and overlap between the clusters. Traditional methods have been extensively studied and used on real-world data, but require users to have some knowledge of the outcome a priori in order to determine how many clusters to look for. Additionally, iterative algorithms choose the optimal number of clusters based on one of several performance measures. In this study, the authors compare the performance of three algorithms (fuzzy c-means, Gustafson-Kessel, and an iterative version of Gustafson-Kessel) when clustering a traditional data set as well as real-world geophysics data that were collected from an archaeological site in Wyoming. Areas of interest in the were identified using a crisp cutoff value as well as a fuzzy <svg style="vertical-align:-0.1638pt;width:9.7749996px;" id="M1" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D6FC" d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204&#xA;q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" /></g></svg>-cut to determine which provided better elimination of noise and non-relevant points. Results indicate that the <svg style="vertical-align:-0.1638pt;width:9.7749996px;" id="M2" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FC" /></g></svg>-cut method eliminates more noise than the crisp cutoff values and that the iterative version of the fuzzy clustering algorithm is able to select an optimum number of subclusters within a point set (in both the traditional and real-world data), leading to proper indication of regions of interest for further expert analysis


David J. Miller

Carl A. Nelson

Molly Boeka Cannon

Kenneth P. Cannon

Comparison of Fuzzy Clustering Methods and Their Applications to Geophysics Data

This paper presents an automatic system of neural networks (NNs) that has the ability to simulate and predict many of applied problems. The system architectures are automatically reorganized and the experimental process starts again, if the required performance is not reached. This processing is continued until the performance obtained. This system is first applied and tested on the two spiral problem; it shows that excellent generalization performance obtained by classifying all points of the two-spirals correctly. After that, it is applied and tested on the shear stress and the pressure drop problem across the short orifice die as a function of shear rate at different mean pressures for linear low-density polyethylene copolymer (LLDPE) at <svg style="vertical-align:-0.20474pt;width:29.637501px;" id="M1" height="13.1875" version="1.1" viewBox="0 0 29.637501 13.1875" width="29.637501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.875)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,12.875)"><path id="x39" d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5&#xA;q53 0 90 28q4 31 4 66q0 51 -9.5 95.5t-39 80.5t-75.5 36z" /></g><g transform="matrix(.017,-0,0,-.017,16.381,12.875)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.012,-0,0,-.012,24.538,4.712)"><path id="x2218" d="M326 255q0 -56 -41 -96t-99 -40t-99 40t-41 96t41 96t99 40t99 -40t41 -96zM274 255q0 38 -25.5 65t-62.5 27t-62.5 -27t-25.5 -65t25.5 -65t62.5 -27t62.5 27t25.5 65z" /></g></svg>C. The system shows a better agreement with an experimental data of the two cases: shear stress and pressure drop. The proposed system has been also designed to simulate other distributions not presented in the training set (predicted) and matched them effectively.

G. M. Behery

A. A. El-Harby

Mostafa Y. El-Bakry

Reorganizing Neural Network System for Two Spirals and Linear Low-Density Polyethylene Copolymer Problems

A focused time lagged recurrent neural network (FTLR NN) with gamma memory filter is designed to learn the subtle complex dynamics of a typical CSTR process. Continuous stirred tank reactor exhibits complex nonlinear operations where reaction is exothermic. It is noticed from literature review that  process control of CSTR using neuro-fuzzy systems was  attempted by many, but optimal neural network model for identification of CSTR process is not yet available. As CSTR process includes temporal relationship in the input-output mappings, time lagged recurrent neural network is particularly used for identification purpose. The standard back propagation algorithm with momentum term has been proposed in this model. The various parameters like number of processing elements, number of hidden layers, training and testing percentage, learning rule and transfer function in hidden and output layer are investigated on the basis of performance measures like MSE, NMSE, and correlation coefficient on testing data set. Finally effects of different norms are tested along with variation in gamma memory filter. It is demonstrated that dynamic NN model has a remarkable system identification capability for the problems considered in this paper. Thus FTLR NN with gamma memory filter can be used to learn underlying highly nonlinear dynamics of the system, which is a major contribution of this paper.

S. N. Naikwad

S. V. Dudul

Identification of a Typical CSTR Using Optimal Focused Time Lagged Recurrent Neural Network Model with Gamma Memory Filter

A neuro-fuzzy controller was designed and
implemented using LabVIEW over a mobile robotic platform.
The controller is based on fuzzy clusters, neural networks, and
search techniques. Also, wireless communication with Bluetooth
protocol was used to communicate the robot with the controller
running in LabVIEW, allowing a simple collaborative task that
consisted in pick and place objects, through knowing the
position of the robot and measuring the distance to the objects.
The neuro-fuzzy controller was split in two parts: the position
controller and the evasion controller against collisions.

Hiram E. Ponce

Dejanira Araiza

Pedro Ponce

A Neuro-Fuzzy Controller for Collaborative Applications in Robotics Using LabVIEW

This study proposes a neural network-family competition genetic algorithm (NN-FCGA) for solving the electromagnetic (EM) optimization and other general-purpose optimization problems. The NN-FCGA is a hybrid evolutionary-based algorithm, combining the good approximation performance of neural network (NN) and the robust and effective optimum search ability of the family competition genetic algorithms (FCGA) to accelerate the optimization process. In this study, the NN-FCGA is used to extract a set of optimal design parameters for two representative design examples: the multiple section low-pass filter and the polygonal electromagnetic absorber. Our results demonstrate that the optimal electromagnetic properties given by the NN-FCGA are comparable to those of the FCGA, but reducing a large amount of computation time and a well-trained NN model that can serve as a nonlinear approximator was developed during the optimization process of the NN-FCGA.

P.-Y. Chen

C.-H. Chen

H. Wang

A Neural Network: Family Competition Genetic Algorithm and Its Applications in Electromagnetic Optimization

Multistep ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in the recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multistep chaotic time series prediction. In the literature there is a wide range of different approaches but their success depends on the predicting performance of the individual methods. Also the most popular neural models are based on the statistical   and   traditional feed forward neural networks. But it is seen that this kind of neural model may present some disadvantages when long-term prediction is required. In this paper focused time-lagged recurrent neural network (FTLRNN) model with gamma memory is developed for different prediction horizons. It is observed that this predictor performs remarkably well for short-term predictions as well as medium-term predictions. For coupled partial differential equations generated chaotic time series such as Mackey Glass and Duffing, FTLRNN-based predictor performs consistently well for different depths of predictions ranging from short term to long term, with only slight deterioration after k is increased beyond 50. For real-world highly complex and nonstationary time series like Sunspots and Laser, though the proposed predictor does perform reasonably for short term and medium-term predictions, its prediction ability drops for long term ahead prediction. However, still this is the best possible prediction results considering the facts that these are nonstationary time series. As a matter of fact, no other NN configuration can match the performance of FTLRNN model. The authors experimented the performance of this FTLRNN model on predicting the dynamic behavior of typical Chaotic Mackey-Glass time series, Duffing time series, and two real-time chaotic time series such as monthly sunspots and laser. Static multi layer perceptron (MLP) model is also attempted and compared against the proposed model on the performance measures like mean squared error (MSE), Normalized mean squared error (NMSE), and Correlation Coefficient (<svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M1" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g></svg>). The standard back-propagation algorithm with momentum term has been used for both the models.

Sanjay L. Badjate

Sanjay V. Dudul

Novel FTLRNN with Gamma Memory for Short-Term and Long-Term Predictions of Chaotic Time Series

Electromyography (EMG) signals can be used for clinical/biomedical application and modern human computer interaction. EMG signals acquire noise while traveling through tissue, inherent noise in electronics equipment, ambient noise, and so forth. ANN approach is studied for reduction of noise in EMG signal. In this paper, it is shown that Focused Time-Lagged Recurrent Neural Network (FTLRNN) can elegantly solve to reduce the noise from EMG signal. After rigorous computer simulations, authors developed an optimal FTLRNN model, which removes the noise from the EMG signal. Results show that the proposed optimal FTLRNN model has an MSE (Mean Square Error) as low as 0.000067 and 0.000048, correlation coefficient as high as 0.99950 and 0.99939 for noise signal and EMG signal, respectively, when validated on the test dataset. It is also noticed that the output of the estimated FTLRNN model closely follows the real one. This network is indeed robust as EMG signal tolerates the noise variance from 0.1 to 0.4 for uniform noise and 0.30 for Gaussian noise. It is clear that the training of the network is independent of specific partitioning of dataset. It is seen that the performance of the proposed FTLRNN model clearly outperforms the best Multilayer perceptron (MLP) and Radial Basis Function NN (RBF) models. The simple NN model such as the FTLRNN with single-hidden layer can be employed to remove noise from EMG signal.

S. N. Kale

Intelligent Noise Removal from EMG Signal Using Focused Time-Lagged Recurrent Neural Network

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Applied Computational Intelligence and Soft Computing