Short-term prediction of chaotic time series by using RBF network with regression weights

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.     

On the structure and initial parameter identification of Gaussian RBF networks

We consider the efficient initialization of structure and parameters of generalized Gaussian radial basis function (RBF) networks using fuzzy decision trees generated by fuzzy ID3 like induction algorithms. The initialization scheme is based on the proposed functional equivalence property of fuzzy decision trees and generalized Gaussian RBF networks. The resulting RBF network is compact, easy to induce, comprehensible, and has acceptable classification accuracy with stochastic gradient descent learning algorithm.     

Enhanced radial basis function neural network for tomato plant disease leaf image segmentation

Primary crop losses in agriculture are due to leaf diseases, which farmers cannot identify early. If the diseases are not detected early and correctly, then the farmer will have to undergo huge losses. Therefore, in the field of agriculture, the detection of leaf diseases in tomato crops plays a vital role. Recent advances in computer vision and deep learning techniques have made disease prediction easy in agriculture. Tomato crop front side leaf images are considered for research due to their high exposure to diseases. The image segmentation process assumes a significant role in identifying disease affected areas on tomato leaf images. Therefore, this paper develops an efficient tomato crop leaf disease segmentation model using an enhanced radial basis function neural network (ERBFNN). The proposed ERBFNN is enhanced using the modified sunflower optimization (MSFO) algorithm. Initially, the noise present in the images is removed by a Gaussian filter followed by CLAHE (contrast-limited adaptive histogram equalization) based on contrast enhancement and un-sharp masking. Then, color features are extracted from each leaf image and given to the segmentation stage to segment the disease portion of the input image. The performance of the proposed ERBFNN approach is estimated using different metrics such as accuracy, Jaccard coefficient (JC), Dice's coefficient (DC), precision, recall, F-Measure, sensitivity, specificity, and mean intersection over union (MIoU) and are compared with existing state-of-the-art methods of radial basis function (RBF), fuzzy c-means (FCM), and region growing (RG). The experimental results show that the proposed ERBFNN segmentation model outperformed with an accuracy of 98.92% compared to existing state-of-the-art methods like RBFNN, FCM, and RG, as well as previous research work.     

Modeling and optimization of microbial hyaluronic acid production by Streptococcus zooepidemicus using radial basis function neural network coupling quantum‐behaved particle swarm optimization algorithm

Hyaluronic acid (HA) is a natural biopolymer with unique physiochemical and biological properties and finds a wide range of applications in biomedical and cosmetic fields. It is important to increase HA production to meet the increasing HA market demand. This work is aimed to model and optimize the amino acids addition to enhance HA production of Streptococcus zooepidemicus with radial basis function (RBF) neural network coupling quantum‐behaved particle swarm optimization (QPSO) algorithm. In the RBF‐QPSO approach, RBF neural network is used as a bioprocess modeling tool and QPSO algorithm is applied to conduct the optimization with the established RBF neural network black model as the objective function. The predicted maximum HA yield was 6.92 g/L under the following conditions: arginine 0.062 g/L, cysteine 0.036 g/L, and lysine 0.043 g/L. The optimal amino acids addition allowed HA yield increased from 5.0 g/L of the control to 6.7 g/L in the validation experiments. Moreover, the modeling and optimization capacity of the RBF‐QPSO approach was compared with that of response surface methodology (RSM). It was indicated that the RBF‐QPSO approach gave a slightly better modeling and optimization result compared with RSM. The developed RBF‐QPSO approach in this work may be helpful for the modeling and optimization of the other multivariable, nonlinear, time‐variant bioprocesses. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, three-layer nets and ME-RBF-SVM models

After introducing the fundamentals of BYY system and harmony learning, which has been developed in past several years as a unified statistical framework for parameter learning, regularization and model selection, we systematically discuss this BYY harmony learning on systems with discrete inner-representations. First, we shown that one special case leads to unsupervised learning on Gaussian mixture. We show how harmony learning not only leads us to the EM algorithm for maximum likelihood (ML) learning and the corresponding extended KMEAN algorithms for Mahalanobis clustering with criteria for selecting the number of Gaussians or clusters, but also provides us two new regularization techniques and a unified scheme that includes the previous rival penalized competitive learning (RPCL) as well as its various variants and extensions that performs model selection automatically during parameter learning. Moreover, as a by-product, we also get a new approach for determining a set of 'supporting vectors' for Parzen window density estimation. Second, we shown that other special cases lead to three typical supervised learning models with several new results. On three layer net, we get (i) a new regularized ML learning, (ii) a new criterion for selecting the number of hidden units, and (iii) a family of EM-like algorithms that combines harmony learning with new techniques of regularization. On the original and alternative models of mixture-of-expert (ME) as well as radial basis function (RBF) nets, we get not only a new type of criteria for selecting the number of experts or basis functions but also a new type of the EM-like algorithms that combines regularization techniques and RPCL learning for parameter learning with either least complexity nature on the original ME model or automated model selection on the alternative ME model and RBF nets. Moreover, all the results for the alternative ME model are also applied to other two popular nonparametric statistical approaches, namely kernel regression and supporting vector machine. Particularly, not only we get an easily implemented approach for determining the smoothing parameter in kernel regression, but also we get an alternative approach for deciding the set of supporting vectors in supporting vector machine.     

A novel hybrid GA/RBFNN technique for protein sequences classification

A novel hybrid genetic algorithm (GA)/radial basis function neural network (RBFNN) technique, which selects features from the protein sequences and trains the RBF neural network simultaneously, is proposed in this paper. Experimental results show that the proposed hybrid GA/RBFNN system outperforms the BLAST and the HMMer.     

Feedforward neural network with adaptive reference pattern layer.

A hybrid neural network architecture is investigated for modeling purposes. The proposed hybrid is based on the multilayer perceptron (MLP) network. In addition to the usual hidden layers, the first hidden layer is selected to be an adaptive reference pattern layer. Each unit in this new layer incorporates a reference pattern that is located somewhere in the space spanned by the input variables. The outputs of these units are the component wise-squared differences between the elements of a reference pattern and the inputs. The reference pattern layer has some resemblance to the hidden layer of the radial basis function (RBF) networks. Therefore the proposed design can be regarded as a sort of hybrid of MLP and RBF networks. The presented benchmark experiments show that the proposed hybrid can provide significant advantages over standard MLPs and RBFs in terms of fast and efficient learning, and compact network structure.     

Culture conditions optimization of hyaluronic acid production by Streptococcus zooepidemicus based on radial basis function neural network and quantum-behaved particle swarm optimization algorithm

This study aimed to optimize the culture conditions (agitation speed, aeration rate and stirrer number) of hyaluronic acid production by Streptococcus zooepidemicus. Two optimization algorithms were used for comparison: response surface methodology (RSM) and radial basis function neural network coupling quantum-behaved particle swarm optimization algorithm (RBF-QPSO). In RBF-QPSO approach, RBF is employed to model the microbial HA production and QPSO algorithm is used to find the optimal culture conditions with the established RBF estimator as the objective function. The predicted maximum HA yield by RSM and RBF-QPSO was 5.27 and 5.62 g/l, respectively, while a maximum HA yield of 5.21 and 5.58 g/l was achieved in the validation experiments under the optimal culture conditions obtained by RSM and RBF-QPSO, respectively. It was indicated that both models provided similar quality predictions for the above three independent variables in terms of HA yield, but RBF model gives a slightly better fit to the measured data compared to RSM model. This work shows that the combination of RBF neural network with QPSO algorithm has good predictability and accuracy for bioprocess optimization and may be helpful to the other industrial bioprocesses optimization to improve productivity.     

支持向量机与神经网络的关系研究

支持向量机是一种基于统计学习理论的新颖的机器学习方法,由于其出色的学习性能,该技术已成为当前国际机器学习界的研究热点,该方法已经广泛用于解决分类和回归问题．本文将结构风险函数应用于径向基函数网络学习中,同时讨论了支持向量回归模型和径向基函数网络之间的关系．仿真实例表明所给算法提高了径向基函数网络的泛化性能．     

Identification of phytoplankton from flow cytometry data by using radial basis function neural networks.

We describe here the application of a type of artificial neural network, the Gaussian radial basis function (RBF) network, in the identification of a large number of phytoplankton strains from their 11-dimensional flow cytometric characteristics measured by the European Optical Plankton Analyser instrument. The effect of network parameters on optimization is examined. Optimized RBF networks recognized 34 species of marine and freshwater phytoplankton with 91. 5% success overall. The relative importance of each measured parameter in discriminating these data and the behavior of RBF networks in response to data from "novel" species (species not present in the training data) were analyzed.     

Hierarchical genetic algorithm for near optimal feedforward neural network design

In this paper, we propose a genetic algorithm based design procedure for a multi layer feed forward neural network. A hierarchical genetic algorithm is used to evolve both the neural networks topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi layer Perceptron networks and radial basis function networks. Based upon the chosen cost function, a linear weight combination decision making approach has been applied to derive an approximated Pareto optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two objective optimization problem.     

Radical pruning: a method to construct skeleton radial basis function networks

Trained radial basis function networks are well-suited for use in extracting rules and explanations because they contain a set of locally tuned units. However, for rule extraction to be useful, these networks must first be pruned to eliminate unnecessary weights. The pruning algorithm cannot search the network exhaustively because of the computational effort involved. It is shown that using multiple pruning methods with smart ordering of the pruning candidates, the number of weights in a radial basis function network can be reduced to a small fraction of the original number. The complexity of the pruning algorithm is quadratic (instead of exponential) in the number of network weights. Pruning performance is shown using a variety of benchmark problems from the University of California, Irvine machine learning database.     

Identification of Phytoplankton from Flow Cytometry Data by Using Radial Basis Function Neural Networks

We describe here the application of a type of artificial neural network, the Gaussian radial basis function (RBF) network, in the identification of a large number of phytoplankton strains from their 11-dimensional flow cytometric characteristics measured by the European Optical Plankton Analyser instrument. The effect of network parameters on optimization is examined. Optimized RBF networks recognized 34 species of marine and freshwater phytoplankton with 91.5% success overall. The relative importance of each measured parameter in discriminating these data and the behavior of RBF networks in response to data from “novel” species (species not present in the training data) were analyzed.     

A fast method for implicit surface reconstruction based on radial basis functions network from 3D scattered points

A method for arbitrary surface reconstruction from 3D large scattered points is proposed in this paper. According to the properties of 3D points, e.g. the non-uniform distribution and unknown topology, an implicit surface model is adopted based on radial basis functions network. And because of the property of locality of radial basis function, the method is fast and robust in surface reconstruction. Furthermore, an adapted K-Means algorithm is used to reduce reconstruction centers. For features completeness, two effective methods are introduced to extract the feature points before the adapted K-Means algorithm. Experiment results show that the presented approach is a good solution for reconstruction from 3D large scattered points.     

A novel approach for short-term load forecasting using support vector machines

A support vector machine (SVM) modeling approach for short-term load forecasting is proposed. The SVM learning scheme is applied to the power load data, forcing the network to learn the inherent internal temporal property of power load sequence. We also study the performance when other related input variables such as temperature and humidity are considered. The performance of our proposed SVM modeling approach has been tested and compared with feed-forward neural network and cosine radial basis function neural network approaches. Numerical results show that the SVM approach yields better generalization capability and lower prediction error compared to those neural network approaches.     

An SOM-based algorithm for optimization with dynamic weight updating

The self-organizing map (SOM), as a kind of unsupervised neural network, has been used for both static data management and dynamic data analysis. To further exploit its search abilities, in this paper we propose an SOM-based algorithm (SOMS) for optimization problems involving both static and dynamic functions. Furthermore, a new SOM weight updating rule is proposed to enhance the learning efficiency; this may dynamically adjust the neighborhood function for the SOM in learning system parameters. As a demonstration, the proposed SOMS is applied to function optimization and also dynamic trajectory prediction, and its performance compared with that of the genetic algorithm (GA) due to the similar ways both methods conduct searches.     

Optimization of auto-induction medium for G-CSF production by Escherichia coli using artificial neural networks coupled with genetic algorithm

Granulocyte colony-stimulating factor (G-CSF) is a cytokine widely used in cancer patients receiving high doses of chemotherapeutic drugs to prevent the chemotherapy-induced suppression of white blood cells. The production of recombinant G-CSF should be increased to meet the increasing market demand. This study aims to model and optimize the carbon source of auto-induction medium to enhance G-CSF production using artificial neural networks coupled with genetic algorithm. In this approach, artificial neural networks served as bioprocess modeling tools, and genetic algorithm (GA) was applied to optimize the established artificial neural network models. Two artificial neural network models were constructed: the back-propagation (BP) network and the radial basis function (RBF) network. The root mean square error, coefficient of determination, and standard error of prediction of the BP model were 0.0375, 0.959, and 8.49 %, respectively, whereas those of the RBF model were 0.0257, 0.980, and 5.82 %, respectively. These values indicated that the RBF model possessed higher fitness and prediction accuracy than the BP model. Under the optimized auto-induction medium, the predicted maximum G-CSF yield by the BP-GA approach was 71.66 %, whereas that by the RBF-GA approach was 75.17 %. These predicted values are in agreement with the experimental results, with 72.4 and 76.014 % for the BP-GA and RBF-GA models, respectively. These results suggest that RBF-GA is superior to BP-GA. The developed approach in this study may be helpful in modeling and optimizing other multivariable, non-linear, and time-variant bioprocesses.     

Neural network models for earthquake magnitude prediction using multiple seismicity indicators

Neural networks are investigated for predicting the magnitude of the largest seismic event in the following month based on the analysis of eight mathematically computed parameters known as seismicity indicators. The indicators are selected based on the Gutenberg-Richter and characteristic earthquake magnitude distribution and also on the conclusions drawn by recent earthquake prediction studies. Since there is no known established mathematical or even empirical relationship between these indicators and the location and magnitude of a succeeding earthquake in a particular time window, the problem is modeled using three different neural networks: a feed-forward Levenberg-Marquardt backpropagation (LMBP) neural network, a recurrent neural network, and a radial basis function (RBF) neural network. Prediction accuracies of the models are evaluated using four different statistical measures: the probability of detection, the false alarm ratio, the frequency bias, and the true skill score or R score. The models are trained and tested using data for two seismically different regions: Southern California and the San Francisco bay region. Overall the recurrent neural network model yields the best prediction accuracies compared with LMBP and RBF networks. While at the present earthquake prediction cannot be made with a high degree of certainty this research provides a scientific approach for evaluating the short-term seismic hazard potential of a region.     

Nonlinear system modelling via optimal design of neural trees

This paper introduces a flexible neural tree model. The model is computed as a flexible multi-layer feed-forward neural network. A hybrid learning/evolutionary approach to automatically optimize the neural tree model is also proposed. The approach includes a modified probabilistic incremental program evolution algorithm (MPIPE) to evolve and determine a optimal structure of the neural tree and a parameter learning algorithm to optimize the free parameters embedded in the neural tree. The performance and effectiveness of the proposed method are evaluated using function approximation, time series prediction and system identification problems and compared with the related methods.