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Negative correlation learning (NCL) is a neural network ensemble learning algorithm that introduces a correlation penalty term to the cost function of each individual network so that each neural network minimizes its mean square error/MSEI together with the correlation of the ensemble. This paper analyzes NCL and reveals that the training of NCL (when λ = 1) corresponds to training the entire ensemble as a single learning machine that only minimizes the MSE without regularization. This analysis explains the reason why NCL is prone to overtitting the noise in the training set. This paper also demonstrates that tuning the correlation parameter λ in NCL by cross validation cannot overcome the overfitting problem. The paper analyzes this problem and proposes the regularized negative correlation learning (RNCL) algorithm which incorporates an additional regularization term for the whole ensemble. RNCL decomposes the ensemble's training objectives, including MSE and regularization, into a set of sub-objectives, and each sub-objective is implemented by an individual neural network. In this paper, we also provide a Bayesian interpretation for RNCL and provide an automatic algorithm to optimize regularization parameters based on Bayesian inference. The RNCL formulation is applicable to any nonlinear estimator minimizing the MSE. The experiments on synthetic as well as real-world data sets demonstrate that RNCL achieves better performance than NCL, especially when the noise level is nontrivial in the data set. [ABSTRACT FROM AUTHOR]

In dealing with large data sets, the reduced support vector machine (RSVM) was proposed for the practical objective to overcome some computational difficulties as well as to reduce the model complexity. In this paper, we study the RSVM from the viewpoint of sampling design, its robustness, and the spectral analysis of the reduced kernel. We consider the nonlinear separating surface as a mixture of kernels. Instead of a full model, the RSVM uses a reduced mixture with kernels sampled from certain candidate set. Our main results center on two major themes. One is the robustness of the random subset mixture model. The other is the spectral analysis of the reduced kernel. The robustness is judged by a few criteria as follows: 1) model variation measure; 2) model bias (deviation) between the reduced model and the full model; and 3) test power in distinguishing the reduced model from the full one. For the spectral analysis, we compare the eigenstructures of the full kernel matrix and the approximation kernel matrix. The approximation kernels are generated by uniform random subsets. The small discrepancies between them indicate that the approximation kernels can retain most of the relevant information for learning tasks in the full kernel. We focus on some statistical theory of the reduced set method mainly in the context of the RSVM. The use of a uniform random subset is not limited to the RSVM. This approach can act as a supplemental algorithm on top of a basic optimization algorithm, wherein the actual optimization takes place on the subset-approximated data. The statistical properties discussed in this paper are still valid. [ABSTRACT FROM AUTHOR]

This paper introduces a general framework for describing dynamic neural networks—the layered digital dynamic network (LDDN). This framework allows the development of two general algorithms for computing the gradients and Jacobians for these dynamic networks: backpropagation-through-time (BPTT) and real-time recurrent learning (RTRL). The structure of the LDDN framework enables an efficient implementation of both algorithms for arbitrary dynamic networks. This paper demonstrates that the BPTT algorithm is more efficient for gradient calculations, but the RTRL algorithm is more efficient for Jacobian calculations. [ABSTRACT FROM AUTHOR]

Original Hebbian encoding scheme of bidirectional associative memory (BAM) provides a poor pattern capacity and recall performance. Based on Rosenblatt's perceptron learning algorithm, the pattern capacity of BAM is enlarged, and perfect recall of all training pattern pairs is guaranteed. However, these methods put their emphases on pattern capacity, rather than error correction capability which is another critical point of BAM. This paper analyzes the sensitivity to noise in RAM and obtains an interesting idea to improve noise immunity of BAM. Some researchers have found that the noise sensitivity of BAM relates to the minimum absolute value of net inputs (MAV). However, in this paper, the analysis on failure association shows that it is related not only to MAV but also to the variance of weights associated with synapse connections. In fact, it is a positive monotone increasing function of the quotient of MAV divided by the variance of weights. This idea provides an useful principle of improving error correction capability of RAM. Some revised encoding schemes, such as small variance learning for RAM (SVBAM), evolutionary pseudorelaxation learning for BAM (EPRLAB) and evolutionary bidirectional learning (EBL), have been introduced to illustrate the performance of this principle. All these methods perform better than their original versions in noise immunity. Moreover, these methods have no negative effect on the pattern capacity of BAM. The convergence of these methods is also discussed in this paper. If there exist solutions, EPRLAB and EBL always converge to a global optimal solution in the senses of both, pattern capacity and noise immunity. However, the convergence of SVBAM may be affected by a preset function. [ABSTRACT FROM AUTHOR]

This paper presents a new sequential learning algorithm for radial basis function (RBF) networks referred to as generalized growing and pruning algorithm for RBF (GGAP-RBF). The paper first introduces the concept of significance for the hidden neurons and then uses it in the learning algorithm to realize parsimonious networks. The growing and pruning strategy of GGAP-RBF is based on linking the required learning accuracy with the significance of the nearest or intentionally added new neuron. Significance of a neuron is a measure of the average information content of that neuron. The GGAP-RBF algorithm can be used for any arbitrary sampling density for training samples and is derived from a rigorous statistical point of view. Simulation re- suits for bench mark problems in the function approximation area show that the GGAP-RBF outperforms several other sequential learning algorithms in terms of learning speed, network size and generalization performance regardless of the sampling density function of the training data. [ABSTRACT FROM AUTHOR]

With the aim of getting understandable symbolic rules to explain a given phenomenon, we split the task of learning these rules from sensory data in two phases: a multilayer perceptron maps features into propositional variables and a set of subsequent layers operated by a PAC-like algorithm learns Boolean expressions on these variables. The special features of this procedure are that: i) the neural network is trained to produce a Boolean output having the principal task of discriminating between classes of inputs; ii) the symbolic part is directed to compute rules within a family that is not known a priori; iii) the welding point between the two learning systems is represented by a feedback based on a suitability evaluation of the computed rules. The procedure we propose is based on a computational learning paradigm set up recently in some papers in the fields of theoretical computer science, artificial intelligence and cognitive systems. The present article focuses on information management aspects of the procedure. We deal with the lack of prior information about the rules through learning strategies that affect both the meaning of the variables and the description length of the rules into which they combine. The paper uses the task of learning to formally discriminate among several emotional states as both a working example and a test bench for a comparison with previous symbolic and subsymbolic methods in the field. [ABSTRACT FROM AUTHOR]

This paper presents a new classifier called total margin-based adaptive fuzzy support vector machines (TAF-SVM) that deals with several problems that may occur in support vector machines (SVMs) when applied to the face recognition. The proposed TAF-SVM not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty, but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm. In addition, by introducing the total margin algorithm to replace the conventional soft margin algorithm, a lower generalization error bound can be obtained. Those three functions are embodied into the traditional SVM so that the TAF-SVM is proposed and reformulated in both linear and nonlinear cases. By using two databases, the Chung Yuan Christian University (CYCU) multiview and the facial recognition technology (FERET) face databases, and using the kernel Fisher's discriminant analysis (KFDA) algorithm to extract discriminating face features, experimental results show that the proposed TAF-SVM is superior to SVM in terms of the face-recognition accuracy. The results also indicate that the proposed TAF-SVM can achieve smaller error variances than SVM over a number of tests such that better recognition stability can be obtained. [ABSTRACT FROM AUTHOR]

This paper presents an asymmetric subset- hood-product fuzzy neural inference system (ASuPFuNIS) that directly extends the SuPFuNIS model [1] by permitting signal and weight fuzzy sets to be modeled by asymmetric Gaussian membership functions. The asymmetric subsethood-product network admits both numeric as well as linguistic inputs. Input nodes, which act as tunable feature fuzzifiers, fuzzify numeric inputs with asymmetric Gaussian fuzzy sets; and linguistic inputs are presented as is. The antecedent and consequent labels of standard fuzzy if-then rules are represented as asymmetric Gaussian fuzzy connection weights of the network. The model uses mutual subsethood based activation spread and a product aggregation operator that works in conjunction with volume defuzzification in a gradient descent learning framework. Despite the increase in the number of free parameters, the proposed model performs better than SuPFuNIS, on various benchmarking problems, both in terms of the performance accuracy and architectural economy and compares excellently with other various existing models with a performance better than most of them. [ABSTRACT FROM AUTHOR]

A new nonlinear feature extraction method called kernel Foley-Sammon optimal discriminant vectors (KFSODVs) is presented in this paper. This new method extends the well-known Foley-Sammon optimal discriminant vectors (FSODVs) from linear domain to a nonlinear domain via the kernel trick that has been used in support vector machine (SVM) and other commonly used kernel-based learning algorithms. The proposed method also provides an effective technique to solve the so-called small sample size (SSS) problem which exists in many classification problems such as face recognition. We give the derivation of KFSODV and conduct experiments on both simulated and real data sets to confirm that the KFSODV method is superior to the previous commonly used kernel-based learning algorithms in terms of the performance of discrimination. [ABSTRACT FROM AUTHOR]

The learning algorithm for complex-bilinear recurrent neural network (C-BLRNN) derived in the paper referenced in the title is incorrect. The correct derivation, which follows the method in two other literatures, is presented. [ABSTRACT FROM AUTHOR]