On the Universal Approximation Theorem of Fuzzy Neural Networks with Random Membership Function Parameters
Lowe [1] proposed that the kernel parameters of a radial basis function (RBF) neural network may first be fixed and the weights of the output layer can then be determined by pseudo-inverse. Jang, Sun, and Mizutani (p.342 ) pointed out that this type of two-step training methods can also be used in fuzzy neural networks (FNNs). By extensive computer simulations, we  demonstrated that an FNN with randomly fixed membership function parameters (FNN-RM) has faster training and better generalization in comparison to the classical FNN. To provide a theoretical basis for the FNN-RM, we present an intuitive proof of the universal approximation ability of the FNN-RM in this paper, based on the orthogonal set theory proposed by Kaminski and Strumillo for RBF neural networks [4].

title: A Novel RBF Neural Network with Fast Training and Accurate Generalization
abstract: For the reason of all the centers and radii needed to be adjusted iteratively, the learning speed of radial basis function (RBF) neural networks is always far slower than required, which obviously forms a bottleneck in many applications. To overcome such problem, we propose a fast and accurate RBF neural network in this paper. First we prove the universal approximation theorem for RBF neural networks with arbitrary centers and radii. Based on this theory, we propose a new learning algorithm called fast and accurate RBF neural network with random kernels (RBF-RK). With the arbitrary centers and radii, our RBF-RK algorithm only needs to adjust the output weights. The experimental results, on function approximation and classification problems, show that the new algorithm not only runs much faster than traditional learning algorithms, but also produces better or at least comparable generalization performance.

title: A Novel Fuzzy Neural Network with Fast Training and Accurate Generalization
abstract: For the reason of all parameters in a conventional fuzzy neural network (FNN) needed to be adjusted iteratively, learning can be very slow and may suffer from local minima. To overcome these problems, we propose a novel FNN in this paper, which shows a fast speed and accurate generalization. First we state the universal approximation theorem for an FNN with random membership function parameters (FNN-RM). Since all the membership function parameters are arbitrarily chosen, the proposed FNN-RM algorithm needs to adjust only the output weights of FNNs. Experimental results on function approximation and classification problems show that the new algorithm not only provides thousands of times of speed-up over traditional learning algorithms, but also produces better generalization performance in comparison to other FNNs.

title: Classification using support vector machines with graded resolution
abstract: A method which we call support vector machine with graded resolution (SVM-GR) is proposed in this paper. During the training of the SVM-GR, we first form data granules to train the SVM-GR and remove those data granules that are not support vectors. We then use the remaining training samples to train the SVM-GR. Compared with the traditional SVM, our SVM-GR algorithm requires fewer training samples and support vectors, hence the computational time and memory requirements for the SVM-GR are much smaller than those of a conventional SVM that use the entire dataset. Experiments on benchmark data sets show that the generalization performance of the SVM-GR is comparable to the traditional SVM.

title: Neural Network Identification Method Applied to the Nonlinear System
abstract: A kind of neural network solution method has been proposed in the paper aiming at a class of non-linear process control system with the characteristic of time delay. In this scheme, a new-type associative memory neural network is used to model the controlled system, and the fuzzy neural network with inverse identification structure is adopted to control the nonlinear process system. This fuzzy neural network control method adopts the structure of three layers combine neural network identifier with inverse structure. Computer simulation and lab application show that it is effective to adopt this scheme to control on-linear process system with time delay.

title: Analog circuit optimization system based on hybrid evolutionary algorithms
abstract: This paper investigates a hybrid evolutionary-based design system for automated sizing of analog integrated circuits (ICs). A new algorithm, called competitive co-evolutionary differential evolution (CODE), is proposed to design analog ICs with practical user-defined specifications. On the basis of the combination of HSPICE and MATLAB, the system links circuit performances, evaluated through electrical simulation, to the optimization system in the MATLAB environment, once a circuit topology is selected. The system has been tested by typical and hard-to-design cases, such as complex analog blocks with stringent design requirements. The results show that the design specifications are closely met, even in highly-constrained situations. Comparisons with available methods like genetic algorithms and differential evolution, which use static penalty functions to handle design constraints, have also been carried out, showing that the proposed algorithm offers important advantages in terms of optimization quality and robustness. Moreover, the algorithm is shown to be efficient.

title: Mining association rules with multiple minimum supports
abstract: Association rule mining is an important model in data mining. Its mining algorithms discover all item associations (or rules) in the data that satisfy the user-specified minimum support (minsup) and minimum confidence (minconf) constraints. Minsup controls the minimum number of data cases that a rule must cover. Minconf controls the predictive strength of the rule. Since only one minsup is used for the whole database, the model implicitly assumes that all items in the data are of the same nature and/or have similar frequencies in the data. This is, however, seldom the case in reallife applications. In many applications, some items appear very frequently in the data, while others rarely appear. If minsup is set too high, those rules that involve rare items will not be found. To find rules that involve both frequent and rare items, minsup has to be set very low. This may cause combinatorial explosion because those frequent items will be associated with one another in all possible ways. This dilemma is called the rare item problem. This paper proposes a novel technique to solve this problem. The technique allows the user to specify multiple minimum supports to reflect the natures of the items and their varied frequencies in the database. In rule mining, different rules may need to satisfy different minimum supports depending on what items are in the rules. Experiment results show that the technique is very effective.

title: Designing Neural Networks Using Hybrid Particle Swarm Optimization
abstract: Evolving artificial neural network is an important issue in both evolutionary computation (EC) and neural networks (NN) fields. In this paper, a hybrid particle swarm optimization (PSO) is proposed by incorporating differential evolution (DE) and chaos into the classic PSO. By combining DE operation with PSO, the exploration and exploitation abilities can be well balanced, and the diversity of swarms can be reasonably maintained. Moreover, by hybridizing chaotic local search (CLS), DE operator and PSO operator, searching behavior can be enriched and the ability to avoid being trapped in local optima can be well enhanced. Then, the proposed hybrid PSO (named CPSODE) is applied to design multi-layer feed-forward neural network. Simulation results and comparisons demonstrate the effectiveness and efficiency of the proposed hybrid PSO.

title: Consensus in Networks of Multiagents With Cooperation and Competition Via Stochastically Switching Topologies
abstract: In this brief, we provide some theoretical analysis of the consensus for networks of agents via stochastically switching topologies. We consider both discrete-time case and continuous-time case. The main contribution of this brief is that the underlying graph topology is more general in both cases than those appeared in previous papers. The weight matrix of the coupling graph is not assumed to be nonnegative or Metzler. That is, in the model discussed here, the off-diagonal entries of the weight matrix of the coupling graph may be negative. This means that sometimes, the coupling may not benefit, but may prevent the consensus of the coupled agents. In the continuous-time case, the switching time intervals also take a more general form of random variables than those appeared in previous works. We focus our study on such networks and give sufficient conditions that ensure almost sure consensus in both discrete-time case and continuous-time case. As applications, we give several corollaries under more specific assumptions, i.e., the switching can be some independent and identically distributed (i.i.d.) random variable series or a Markov chain. Numerical examples are also provided in both discrete-time and continuous-time cases to demonstrate the validity of our theoretical results.