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Extreme learning machine (ELM) is a non-iterative algorithm for training single-hidden layer feed-forward networks, whose training speed is much faster than those of conventional neural networks. However, its objective is only to minimize the empirical risk, which may cause overfitting easily. To overcome this defect, this paper proposes a novel algorithm named LGE2LM based on the localized generalization error model which provides an upper bound of generalization error through adopting the stochastic sensitivity. LGE2LM aims to improve the generalization capability of ELM by using the regularization technique which makes a trade-off between the empirical risk and the stochastic sensitive measure. The essence of LGE2LM is a quadratic problem without iterative process. Similar to ELM, all the parameters of this new algorithm are obtained without tuning, which makes the efficiency of LGE2LM much higher than those of traditional neural networks. Several experiments conducted on both artificial and real-world datasets show that LGE2LM has much better generalization capability and stronger robustness in comparison with ELM. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence theorems that are associated with a Discrete Hopfield Neural Network (DHNN) with delay. We present two updating rules, one for serial mode and the other for parallel mode. The speed of convergence of these proposed updating rules is faster than all of the existing updating rules. It has been proved in this paper that a DHNN with delay will converge to a stable state when operating in a serial mode if the matrix of weights of the no-delay term is symmetric. In addition, it has been proved that they will converge to a stable state when operating in a parallel mode if the matrix of weights of the no-delay term is a symmetric and non-negative definite matrix. The condition for convergence of a DHNN without delay can been relaxed from the need to have a symmetric matrix to an even weaker condition of having a quasi-symmetric matrix. The results in this paper extend both the existing results concerning the convergence of a DHNN without delay and our previous findings. By means of the new network structure and its convergence theorems, we propose a local searching algorithm for combinatorial optimization. We also relate the maximum value of a bivariate energy function to the stable states of a DHNN with delay, which generalizes Hopfield's energy function. Moreover, for the serial model we give the relationship between the convergence of the energy function and the convergence of the corresponding network. One application is presented to demonstrate the higher rate of convergence and the accuracy of the classification using our algorithm. [ABSTRACT FROM AUTHOR]

Fuzzy production rules (FPRs) have been used for years to capture and represent fuzzy, vague, imprecise and uncertain domain knowledge in many fuzzy systems. There have been a lot of researches on how to generate or obtain FPRs. There exist two methods to obtain FPRs. One is by painstakingly, repeatedly and time-consuming interviewing domain experts to extract the domain knowledge. The other is by using some machine learning techniques to generate and extract FPRs from some training samples. These extracted rules, however, are found to be nonoptimal and sometimes redundant. Furthermore, these generated rules suffer from the problem of low accuracy of classifying or recognizing unseen examples. The reasons for having these problems are 1) the FPRs generated are not powerful enough to represent the domain knowledge, 2) the techniques used to generate FPRs are pre-matured, ad-hoc or may not be suitable for the problem, and 3) further refinement of the extracted rules has not been done. In this paper we look into the solutions of the above problems by 1) enhancing the representation power of FPRs by including local and global weights, 2) developing a fuzzy neural network (FNN) with enhanced learning algorithm, and 3) using this FNN to refine the local and global weights of FPRs. By experimenting our method with some existing benchmark examples, the proposed method is found to have high accuracy in classifying unseen samples without increasing the number of the FPRs extracted and the time required to consult with domain experts is greatly reduced. [ABSTRACT FROM AUTHOR]

We had developed the localized generalization error model for supervised learning with minimization of Mean Square Error. In this work, we extend the error model to Single Layer Perceptron Neural Network (SLPNN) and Support Vector Machine (SVM) with sigmoid kernel function. For a trained SLPNN or SVM and a given training dataset, the proposed error model bounds above the error for unseen samples which are similar to the training samples. As the major component of the localized generalization error model, the stochastic sensitivity measure formula for perceptron neural network derived in this work has relaxed the assumptions of same distribution for all inputs and each sample perturbed only once in previous works. These make the sensitivity measure applicable to pattern classification problems. The stochastic sensitivity measure of SVM with Sigmoid kernel is also derived in this work as a component of the localized generalization error model. At the end of this paper, we discuss the advantages of the proposed error bound over existing error bound. [ABSTRACT FROM AUTHOR]

In this paper, the Hopfield neural network with delay (HNND) is studied from the standpoint of regarding it as an optimizing computational model. Two general updating rules for networks with delay (GURD) are given based on Hopfield-type neural networks with delay for optimization problems and characterized by dynamic thresholds. It is proved that in any sequence of updating rule modes, the GURD monotonously converges to a stable state of the network. The diagonal elements of the connection matrix are shown to have an important influence on the convergence process, and they represent the relationship of the local maximum value of the energy function to the stable states of the networks. All the ordinary discrete Hopfield neural network (DHNN) algorithms are instances of the GURD. It can be shown that the convergence conditions of the GURD may be relaxed in the context of applications, for instance, the condition of nonnegative diagonal elements of the connection matrix can be removed from the original convergence theorem. A new updating rule mode and restrictive conditions can guarantee the network to achieve a local maximum of the energy function with a step-by-step algorithm. The convergence rate improves evidently when compared with other methods. For a delay item considered as a noise disturbance item, the step-by-step algorithm demonstrates its efficiency and a high convergence rate. Experimental results support our proposed algorithm. [ABSTRACT FROM AUTHOR]

Multiple Classifier System (MCS) is a very popular research topic in recent years. It has been proved theoretically and empirically to be better than single classifiers in many scenarios. Creating diverse sets of classifier is one of the key issues in building MCSs. Feature grouping is one of the methods to create diverse classifiers and it has been shown to improve the accuracy of an MCS. In this paper, we propose a new feature grouping method based on Genetic Algorithm (GA) with the localized Generalization Error Model as the evaluation criterion. The combined individual classifiers using the weighted sum are examined in this paper. Moreover, several feature grouping methods are compared with the proposed method in this work. The experimental results on benchmark dataset show that the MCS trained by the proposed method is promising. [ABSTRACT FROM AUTHOR]