Optimal Number Of Hidden Nodes Research Articles

Multivariable Dynamic Modeling for Molten Iron Quality Using Incremental Random Vector Functional-link Networks

Molten iron temperature as well as Si, P, and S contents is the most essential molten iron quality (MIQ) indices in the blast furnace (BF) ironmaking, which requires strict monitoring during the whole ironmaking production. However, these MIQ parameters are difficult to be directly measured online, and large-time delay exists in off-line analysis through laboratory sampling. Focusing on the practical challenge, a data-driven modeling method was presented for the prediction of MIQ using the improved multivariable incremental random vector functional-link networks (M-I-RVFLNs). Compared with the conventional random vector functional-link networks (RVFLNs) and the online sequential RVFLNs, the M-I-RVFLNs have solved the problem of deciding the optimal number of hidden nodes and overcome the overfitting problems. Moreover, the proposed M-I-RVFLNs model has exhibited the potential for multivariable prediction of the MIQ and improved the terminal condition for the multiple-input multiple-output (MIMO) dynamic system, which is suitable for the BF ironmaking process in practice. Ultimately, industrial experiments and contrastive researches have been conducted on the BF No. 2 in Liuzhou Iron and Steel Group Co. Ltd. of China using the proposed method, and the results demonstrate that the established model produces better estimating accuracy than other MIQ modeling methods.

SVM–ELM: Pruning of Extreme Learning Machine with Support Vector Machines for Regression

AbstractExtreme Learning Machine provides very competitive performance to other related classical predictive models for solving problems such as regression, clustering, and classification. An ELM possesses the advantage of faster computational time in both training and testing. However, one of the main challenges of an ELM is the selection of the optimal number of hidden nodes. This paper presents a new approach to node selection of an ELM based on a 1-norm support vector machine (SVM). In this method, the targets of SVM yi ∈{+1, –1} are derived using the mean or median of ELM training errors as a threshold for separating the training data, which are projected to SVM dimensions. We present an integrated architecture that exploits the sparseness in solution of SVM to prune out the inactive hidden nodes in ELM. Several experiments are conducted on real-world benchmark datasets, and the results attained attest to the efficiency of the proposed method.

Ant Colony Algorithm Based on Improved Neural Network Algorithm and its Application

This paper mainly to the ant colony algorithm ant colony system (application pseudo-random proportional rules) and add adaptive learning, momentum BP algorithm of these three together was improved, established a hybrid algorithm, to a certain extent overcome the BP algorithm is easy to fall into local minimum value, slow convergence speed, and achieved satisfactory results. Generally speaking, the performance of BP network is composed of two components: the topology of the network and network learning algorithm. The topology of the network design especially hidden node number should be how to choose the number of neurons more reasonable there is no unified theory, the solution actual problem at present is more of the experience and the method of combining the test to determine the optimal number of hidden nodes. This paper mainly discussed the structure of neural network to determine later, network learning process problems.

Fast and Robust Method for Dynamic Gesture Recognition Using Hermite Neural Network

Due to its shortcomings such as slow convergence rate and low recognition accuracy, the traditional BP neural networks perform poorly in dynamic gesture recognition, especially for online gesture training. In this paper, a novel adaptive Hermite neural networks algorithm for dynamic gesture recognition was proposed. At first, a three-layer feed-forward neural network, of which hidden layer neurons are activated by a group of Hermite orthogonal polynomial functions was constructed. Based on its special structure, a method to determine the network weights directly was introduced, and a novel algorithm to determine the optimal number of hidden nodes adaptively was proposed. Then a rapid method of fingertips tracking was put forward to get the trajectory of dynamic gesture. At last, dynamic gesture was recognized through the trained Hermite neural network. Experiment results show that Hermite neural network can enhance the speed and precision of network training, improve the learning speed and recognition accuracy, and has good robustness and generalization ability.

Hidden Node Optimization for Extreme Learning Machine

The number of hidden nodes is a critical factor for the generalization of ELM. Generally, it is heavy for time consumption to obtain the optimal number of hidden nodes with trial-and-error. A novel algorithm is proposed to optimize the hidden node number to guarantee good generalization, which employs the PSO in the optimization process with structural risk minimization principle. The simulation results indicate our algorithm for the optimal number of hidden nodes is reasonable and feasible with 6 datasets on benchmark problems by the accuracy comparisons.

Application of Genetic Algorithm Optimized Neural Network Connection Weights for Medical Diagnosis of PIMA Indians Diabetes

Neural Networks are one of many data mining analytical tools that can be utilized to make predictions for medical data. Model selection for a neural network entails various factors such as selection of the optimal number of hidden nodes, selection of the relevant input variables and selection of optimal connection weights. This paper presents the application of hybrid model that integrates Genetic Algorithm and Back Propatation network(BPN) where GA is used to initialize and optmize the connection weights of BPN . Significant feactures identified by using two methods :Decision tree and GA-CFS method are used as input to the hybrid model to diagonise diabetes mellitus. The results prove that, GA-optimized BPN approach has outperformed the BPN approach without GA optimization. In addition the hybrid GA-BPN with relevant inputs lead to further improvised categorization accuracy compared to results produced by GA-BPN alone with some redundant inputs.

Constructive hidden nodes selection of extreme learning machine for regression

In this paper, we attempt to address the architectural design of ELM regressor by applying a constructive method on the basis of ELM algorithm. After the nonlinearities of ELM network are fixed by randomly generating the parameters, the network will correspond to a linear regression model. The selection of hidden nodes can then be regarded as a subset model selection in linear regression. The proposed constructive hidden nodes selection for ELM (referred to as CS-ELM) selects the optimal number of hidden nodes when the unbiased risk estimation based criterion C P reaches the minimum value. A comparison of the proposed CS-ELM with other model selection algorithms of ELM is evaluated on several real benchmark regression applications. And the empirical study shows that CS-ELM leads to a compact network structure automatically.

Constructing input to neural networks for modeling temperature-caused modal variability: Mean temperatures, effective temperatures, and principal components of temperatures

In this study, the construction of appropriate input to neural networks for modeling the temperature-caused modal variability is addressed with intent to enhance the reproduction and prediction capabilities of the formulated correlation models. Available for this study are 770 h modal frequency and temperature data that were obtained from the instrumented cable-stayed Ting Kau Bridge in Hong Kong. With the temperature data measured at different portions of the bridge, three kinds of input, i.e., mean temperatures, effective temperatures, and principal components (PCs) of temperatures, are constructed as input to neural networks for modeling the correlation between the modal frequencies and environmental temperatures. By dividing the 770 h modal frequency and temperature data into training data set, validation data set and testing data set, an optimally configured back-propagation neural network (BPNN) is formulated for each kind of input, in which the validation data are utilized to determine the optimal number of hidden nodes while the early stopping technique is applied to optimize the BPNN parameters. Then the reproduction and prediction performance of the BPNNs configured with the three kinds of input is examined and compared in respect of the seen training data set and the unseen testing data set, respectively. It is revealed that the temperature profile characterized by the effective temperatures is insufficient for formulating a good correlation model between the modal frequencies and temperatures. When a sufficient number of PCs are used, the BPNN with input of the PCs of temperatures performs better than the BPNN with input of the mean temperatures in both reproduction and prediction capabilities.

Rainfall‐runoff modelling using artificial neural networks: comparison of network types

AbstractGrowing interest in the use of artificial neural networks (ANNs) in rainfall‐runoff modelling has suggested certain issues that are still not addressed properly. One such concern is the use of network type, as theoretical studies on a multi‐layer perceptron (MLP) with a sigmoid transfer function enlightens certain limitations for its use. Alternatively, there is a strong belief in the general ANN user community that a radial basis function (RBF) network performs better than an MLP, as the former bases its nonlinearities on the training data set. This argument is not yet substantiated by applications in hydrology. This paper presents a comprehensive evaluation of the performance of MLP‐ and RBF‐type neural network models developed for rainfall‐runoff modelling of two Indian river basins. The performance of both the MLP and RBF network models were comprehensively evaluated in terms of their generalization properties, predicted hydrograph characteristics, and predictive uncertainty. The results of the study indicate that the choice of the network type certainly has an impact on the model prediction accuracy. The study suggests that both the networks have merits and limitations. For instance, the MLP requires a long trial‐and‐error procedure to fix the optimal number of hidden nodes, whereas for an RBF the structure of the network can be fixed using an appropriate training algorithm. However, a judgment on which is superior is not clearly possible from this study. Copyright © 2004 John Wiley & Sons, Ltd.

Symbolic classification, clustering and fuzzy radial basis function network

Symbolic fuzzy classification is proposed using fuzzy radial basis function network, with fuzzy c-medoids clustering at the hidden layer. Symbolic objects include linguistic, nominal, boolean and interval-type of features, along with quantitative attributes. Classification and clustering in this domain involve the use of symbolic dissimilarity between the objects. Fuzzy memberships are used for appropriately handling uncertainty inherent in real-life decisions. The fuzzy radial basis function (FRBF) network here comprises an integration of the principles of radial basis function (RBF) network and fuzzy c-medoids clustering, for handling non-numeric data. The optimal number of hidden nodes is determined by using clustering validity indices, like normalized modified Hubert's statistic and Davies–Bouldin index, in the symbolic framework. The effectiveness of the symbolic fuzzy classification is demonstrated on real-life benchmark data sets. Comparison is provided with the performance of a decision tree.

Partial least-squares algorithm for weights initialization of backpropagation network

This paper proposes a hybrid scheme to set the weights initialization and the optimal number of hidden nodes of the backpropagation network (BPN) by applying the loading weights and factor numbers of the partial least-squares (PLS) algorithm. The joint PLS and BPN method (PLSBPN) starts with a small residual error, modifies the latent weight matrices, and obtains a near-global minimum in the calibration phase. Performances of the BPN, PLS, and PLSBPN were compared for the near infrared spectroscopic analysis of glucose concentrations in aqueous matrices. The results showed that the PLSBPN had the smallest root mean square error. The PLSBPN approach significantly solves some conventional problems of the BPN method by providing the good initial weights, reducing the calibration time, obtaining an optimal solution, and easily determining the number of hidden nodes.

Rough knowledge-based network, fuzziness and classification

A method of integrating rough sets and fuzzy multilayer perceptron (MLP) for designing a knowledge-based network for pattern recognition problems is described. Rough set theory is used to extract crude knowledge from the input domain in the form of rules. The syntax of these rules automatically determines the optimal number of hidden nodes while the dependency factors are used in the initial weight encoding. Results on classification of speech data demonstrate the superiority of the system over the fuzzy and conventional versions of the MLP.