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In this paper, we argue that for a C-class classification problem, C 2-class classifiers, each of which discriminating one class from the other classes and having a characteristic input feature subset, should in general outperform, or at least match the performance of, a C-class classifier with one single input feature subset. For each class, we select a desirable feature subset, which leads to the lowest classification error rate for this class using a classifier for a given feature subset search algorithm. To fairly compare all models, we propose a weight method for the class-dependent classifier, i.e., assigning a weight to each model's output before the comparison is carried out. The method's performance is evaluated on two artificial data sets and several real-world benchmark data sets, with the support vector machine (SVM) as the classifier , and with the RELIEF, class separability, and minimal-redundancy-maximal-relevancy (mRMR) as attribute importance measures. Our results indicate that the class-dependent feature subsets found by our approach can effectively remove irrelevant or redundant features, while maintaining or improving (sometimes substantially ) the classification accuracy, in comparison with other feature selection methods.

Chen and Aihara recently proposed a chaotic simulated annealing approach to solving optimization problems. By adding a negative self-coupling to a network model proposed earlier by Aihara et al. and gradually removing this negative self-coupling, they used the transient chaos for searching and self-organizing, thereby achieving remarkable improvement over other neural-network approaches to optimization problems with or without simulated annealing. In this paper we suggest a new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function by gradually reducing the time step in the Euler approximation of the differential equations that describe the continuous Hopfield neural network. This approach eliminates the need to carefully select other system parameters. We also generalize the convergence theorems of Chen and Aihara to arbitrarily increasing neuronal input-output functions and to less restrictive and yet more compact forms.

Autoassociations of spatio-temporal sequences have been discussed by a number of authors. We propose a mechanism for storing and retrieving pairs of spatio-temporal sequences with the network architecture of the standard bidirectional associative memory (BAM), thereby achieving hetero-associations of spatio-temporal sequences.

In this paper, we propose a gradual noisy chaotic neural network (G-NCNN) to solve the NP-complete broadcast scheduling problem (BSP) in packet radio networks. The objective of the BSP is to design an optimal time-division multiple-access (TDMA) frame structure with minimal TDMA frame length and maximal channel utilization. A two-phase optimization is adopted to achieve the two objectives with two different energy functions, so that the G-NCNN not only finds the minimum TDMA frame length but also maximizes the total node transmissions. In the first phase, we propose a G-NCNN which combines the noisy chaotic neural network (NCNN) and the gradual expansion scheme to find a minimal TDMA frame length. In the second phase, the NCNN is used to find maximal node transmissions in the TDMA frame obtained in the first phase. The performance is evaluated through several benchmark examples and 600 randomly generated instances. The results show that the G-NCNN outperforms previous approaches, such as mean field annealing, a hybrid Hopfield network-genetic algorithm, the sequential vertex coloring algorithm, and the gradual neural network.

This comment letter points out that the essence of the ldquoextreme learning machine (ELM)rdquo recently appeared has been proposed earlier by Broomhead and Lowe and Pao , and discussed by other authors. Hence, it is not necessary to introduce a new name "ELM".

We derive learning rates such that all training patterns are equally important statistically and the learning outcome is independent of the order in which training patterns are presented, if the competitive neurons win the same sets of training patterns regardless the order of presentation. We show that under these schemes, the learning rules in the two different weight normalization approaches, the length-constraint and the sum-constraint, yield practically the same results, if the competitive neurons win the same sets of training patterns with both constraints. These theoretical results are illustrated with computer simulations.

We present convergence theorems for neural networks with arbitrary energy functions and discrete-time dynamics for both discrete and continuous neuronal input-output-functions. We discuss systematically how the neuronal updating rule should be extracted once an energy function is constructed for a given application, in order to guarantee the descent and minimization of the energy function as the network updates. We explain why the existing theory may lead to inaccurate results and oscillatory behaviors in the convergence process. We also point out the reason for and the side effects of using hysteresis neurons to suppress these oscillatory behaviors.

This paper studies the effects of a time-dependent operating environment on the dynamics of a neural network. In the previous paper Wang et al. (1990) studied an exactly solvable model of a higher order neural network. We identified a bifurcation parameter for the system, i.e., the rescaled noise level, which represents the combined effects of incomplete connectivity, interference among stored patterns, and additional stochastic noise. When this bifurcation parameter assumes different but static (time-independent) values, the network shows a spectrum of dynamics ranging from fixed points, to oscillations, to chaos. This paper shows that varying operating conditions described by the time-dependence of the rescaled noise level give rise to many more interesting dynamical behaviours, such as disappearances of fixed points and transitions between periodic oscillations and deterministic chaos. These results suggest that a varying environment, such as the one studied in the present model, may be used to facilitate memory retrieval if dynamic states are used for information storage in a neural network.