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Training of recurrent neural networks (RNNs) introduces considerable computational complexities due to the need for gradient evaluations. How to get fast convergence speed and low computational complexity remains a challenging and open topic. Besides, the transient response of learning process of RNNs is a critical issue, especially for online applications. Conventional RNN training algorithms such as the backpropagation through time and real-time recurrent learning have not adequately satisfied these requirements because they often suffer from slow convergence speed. If a large learning rate is chosen to improve performance, the training process may become unstable in terms of weight divergence. In this paper, a novel training algorithm of RNN, named robust recurrent simultaneous perturbation stochastic approximation (RRSPSA), is developed with a specially designed recurrent hybrid adaptive parameter and adaptive learning rates. RRSPSA is a powerful novel twin-engine simultaneous perturbation stochastic approximation (SPSA) type of RNN training algorithm. It utilizes three specially designed adaptive parameters to maximize training speed for a recurrent training signal while exhibiting certain weight convergence properties with only two objective function measurements as the original SPSA algorithm. The RRSPSA is proved with guaranteed weight convergence and system stability in the sense of Lyapunov function. Computer simulations were carried out to demonstrate applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

Linear regression uses the least square algorithm to solve the solution of linear regression equation. Linear regression classification (LRC) shows good classification performance on face image data. However, when the axes of linear regression of class-specific samples have intersections, LRC could not well classify the samples that distribute around intersections. Moreover, the LRC could not perform well at the situation of severe lighting variations. This paper proposes a new classification method, kernel linear regression classification (KLRC), based on LRC and the kernel trick. KLRC is a nonlinear extension of LRC and can offset the drawback of LRC. KLRC implicitly maps the data into a high-dimensional kernel space by using the nonlinear mapping determined by a kernel function. Through this mapping, KLRC is able to make the data more linearly separable and can perform well for face recognition with varying lighting. For comparison, we conduct on three standard databases under some evaluation protocols. The proposed methodology not only outperforms LRC but also takes the better performance than typical kernel methods such as kernel linear discriminant analysis and kernel principal component analysis. [ABSTRACT FROM AUTHOR]

Motivated by the support vector data description, a classical one-class support vector machine, and the twin support vector machine classifier, this paper formulates a twin support vector hypersphere (TSVH) classifier, a novel binary support vector machine (SVM) classifier that determines a pair of hyperspheres by solving two related SVM-type quadratic programming problems, each of which is smaller than that of a conventional SVM, which means that this TSVH is more efficient than the classical SVM. In addition, the TSVH successfully avoids matrix inversion compared with the twin support vector machine, which indicates learning algorithms of the SVM can be easily extended to this TSVH. Computational results on several synthetic as well as benchmark data sets indicate that the proposed TSVH is not only faster, but also obtains better generalization. [ABSTRACT FROM AUTHOR]

Clustering is often considered as an unsupervised data analysis method, but making full use of the prior information in the process of clustering will significantly improve the performance of the clustering algorithm. Spectral clustering algorithm can well use the prior pairwise constraint information to cluster and has become a new hot spot of machine learning research in recent years. In this paper, we propose an effective clustering algorithm, called a semi-supervised spectral clustering algorithm based on pairwise constraints, in which the similarity matrix of data points is adjusted and optimized by pairwise constraints. The experiments on real-world data sets demonstrate the effectiveness of this algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigated an approach for robots to learn to adapt dance actions to human's preferences through interaction and feedback. Human's preferences were extracted by analysing the common action patterns with positive or negative feedback from the human during robot dancing. By using a buffering technique to store the dance actions before a feedback, each individual's preferences can be extracted even when a reward is received late. The extracted preferred dance actions from different people were then combined to generate improved dance sequences, i.e. performing more of what was preferred and less of that was not preferred. Together with Softmax action-selection method, the Sarsa reinforcement learning algorithm was used as the underlining learning algorithm and to effectively control the trade-off between exploitation of the learnt dance skills and exploration of new dance actions. The results showed that the robot learnt, using interactive reinforcement learning, the preferences of human partners, and the dance improved with the extracted preferences from more human partners. [ABSTRACT FROM AUTHOR]

Mamdani-type inference systems with trapezoidal-shaped fuzzy membership functions play a crucial role in a wide variety of engineering systems, including real-time control, transportation and logistics, network management, etc. The automatic identification or construction of such fuzzy systems input output data is one of the key problems in modeling. In the past years, the authors have investigated several different fuzzy t-norms, among others, algebraic and trigonometric ones, and the Hamacher product by substituting the standard 'min' t-norm operation, in order to achieve better model fitting. In the present paper, the focus is on examining the general parametric Hamacher t-norm, where the free parameter quite essentially influences the quality of modeling and the learning capability of the model identification system. Based on a wide scope of simulation experiments, a quasi-optimal interval for the value of the Hamacher operator is proposed. [ABSTRACT FROM AUTHOR]

Sample misalignment exerts an important influence on training a rapid and accurate human detector, and it is a difficult problem to tackle with due to human articulation or manual annotation errors. Multiple instances learning method is an effective tool to deal with this difficulty without manual correction. In this paper, firstly, we propose a variable granularity HOG-CSLBP feature, which combines the human shape information with local texture information, and encodes spatial relationship in different granularity to improve its discriminative ability. Our new feature takes an advantage of the mutual complementarities of histogram of gradient and center-symmetric local binary patterns feature, which is adept at modeling human. Secondly, we present a Gentle MILBoost algorithm which utilizes the Newton update technique to get an optimal weak classifier that is able to discriminate complex distribution and is more stable in numerical computation. Experimental results based on INRIA, MIT-CBCL and TUD-Brussels datasets have showed superior performance of our method. Moreover, our method can achieve real-time speed in real application. [ABSTRACT FROM AUTHOR]

Multi-instance learning was first proposed by Dietterich et al. (Artificial Intelligence 89(1–2):31–71, 1997 ) when they were investigating the problem of drug activity prediction. Here, the training set is composed of labeled bags, each of which consists of many unlabeled instances. And the goal of this learning framework is to learn some classifier from the training set for correctly labeling unseen bags. After Dietterich et al., many studies about this new learning framework have been started and many new algorithms have been proposed, for example, DD, EM-DD, Citation- kNN and so on. All of these algorithms are working on the full data set. But as in single-instance learning, different feature in training set has different effect on the training about classifier. In this paper, we will study the problem about feature selection in multi-instance learning. We will extend the data reliability measure and make it select the key feature in multi-instance scenario. [ABSTRACT FROM AUTHOR]

Regularized multiple criteria linear programming (RMCLP) model is a new powerful method for classification and has been used in various real-life data mining problems. In this paper, a new Multi-instance Classification method based on RMCLP was proposed (called MI-RMCLP), which includes two algorithms for linearly separable case and nonlinearly case separately. The key point of this method, instead of a mixed integer quadratic programming in MI-SVM, is that it is able to deal with multi-instance learning problem by an iterative strategy solving sequential quadratic programming problems. All experiment results have shown that MI-RMCLP method can converge to the optimal value in limited iterative steps and be a competitive method in multi-instance learning classification. [ABSTRACT FROM AUTHOR]

Privacy preserving data mining algorithms are proposed to protect the participating parties' data privacy in data mining processes. So far, most of these algorithms only work in the semi-honest model that assumes all parties follow the algorithms honestly. In this paper, we propose two privacy preserving perceptron learning algorithms in the malicious model, for horizontally and vertically partitioned data sets, respectively. So far as we know, our algorithms are the first perceptron learning algorithms that can protect data privacy in the malicious model. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm that enhances speech by independent vector analysis (IVA) using harmonic frequency dependency for robust speech recognition. While the conventional IVA exploits the full-band uniform dependencies of each source signal, a harmonic clique model is introduced to improve the enhancement performance by modeling strong dependencies among multiples of fundamental frequencies. An IVA-based learning algorithm is derived to consider the non-holonomic constraint and the minimal distortion principle to reduce the unavoidable distortion of IVA, and the minimum power distortionless response beamformer is used as a pre-processing step. In addition, the algorithm compares the log-spectral features of the enhanced speech and observed noisy speech to identify time-frequency segments corrupted by noise and restores those with the cluster-based missing feature reconstruction technique. Experimental results demonstrate that the proposed method enhances recognition performance significantly in noisy environments, especially with competing interference. [ABSTRACT FROM AUTHOR]

Most state-of-the-art speaker recognition systems are based on discriminative learning approaches. On the other hand, generative Gaussian mixture models (GMM) have been widely used in speaker recognition during the last decades. In an earlier work, we proposed an algorithm for discriminative training of GMM with diagonal covariances under a large margin criterion. In this paper, we propose an improvement of this algorithm, which has the major advantage of being computationally highly efficient, thus well suited to handle large-scale databases. We also develop a new strategy to detect and handle the outliers that occur in the training data. To evaluate the performances of our new algorithm, we carry out full NIST speaker identification and verification tasks using NIST-SRE'2006 data, in a Symmetrical Factor Analysis compensation scheme. The results show that our system significantly outperforms the traditional discriminative support vector machines (SVM)-based system of SVM-GMM supervectors, in the two speaker recognition tasks. [ABSTRACT FROM AUTHOR]

Metric learning has been widely studied in machine learning due to its capability to improve the performance of various algorithms. Meanwhile, multi-task learning usually leads to better performance by exploiting the shared information across all tasks. In this paper, we propose a novel framework to make metric learning benefit from jointly training all tasks. Based on the assumption that discriminative information is retained in a common subspace for all tasks, our framework can be readily used to extend many current metric learning methods. In particular, we apply our framework on the widely used Large Margin Component Analysis (LMCA) and yield a new model called multi-task LMCA. It performs remarkably well compared to many competitive methods. Besides, this method is able to learn a low-rank metric directly, which effects as feature reduction and enables noise compression and low storage. A series of experiments demonstrate the superiority of our method against three other comparison algorithms on both synthetic and real data. [ABSTRACT FROM AUTHOR]

In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the twin support vector regression (TSVR) is proposed. Though at the outset the algorithm requires inverse of matrices, it has been shown that they would be obtained by performing matrix subtraction of the identity matrix by a scalar multiple of inverse of a positive semi-definite matrix that arises in the original formulation of TSVR. The algorithm can be easily implemented and does not need any optimization packages. To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world datasets. Similar or better generalization performance of the proposed method in less training time in comparison with the standard and twin support vector regression methods clearly exhibits its suitability and applicability. [ABSTRACT FROM AUTHOR]

Distributed training allows individual entities to benefit from the training sets owned by other entities. Nevertheless, distributed training also causes serious privacy concerns. Hence, it is highly important to protect privacy in distributed training. In this paper, we study the privacy protection in distributed training of neural network ensembles. We design a privacy-preserving distributed algorithm for training neural network ensembles using AdaBoost.M2. We also analyze the security and complexity of our algorithm. Furthermore, we perform experiments on two data sets of the UCI repository to verify the algorithm's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, extreme learning machine (ELM) for ε-insensitive error loss function-based regression problem formulated in 2-norm as an unconstrained optimization problem in primal variables is proposed. Since the objective function of this unconstrained optimization problem is not twice differentiable, the popular generalized Hessian matrix and smoothing approaches are considered which lead to optimization problems whose solutions are determined using fast Newton-Armijo algorithm. The main advantage of the algorithm is that at each iteration, a system of linear equations is solved. By performing numerical experiments on a number of interesting synthetic and real-world datasets, the results of the proposed method are compared with that of ELM using additive and radial basis function hidden nodes and of support vector regression (SVR) using Gaussian kernel. Similar or better generalization performance of the proposed method on the test data in comparable computational time over ELM and SVR clearly illustrates its efficiency and applicability. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) rely on global positioning system (GPS) information to ascertain its position for navigation during mission execution. In the absence of GPS information, the capability of a UAV to carry out its intended mission is hindered. In this paper, we learn alternative means for UAVs to derive real-time positional reference information so as to ensure the continuity of the mission. We present extreme learning machine as a mechanism for learning the stored digital elevation information so as to aid UAVs to navigate through terrain without the need for GPS. The proposed algorithm accommodates the need of the on-line implementation by supporting multi-resolution terrain access, thus capable of generating an immediate path with high accuracy within the allowable time scale. Numerical tests have demonstrated the potential benefits of the approach. [ABSTRACT FROM AUTHOR]

In this paper, the classification of the two binary bioinformatics datasets, leukemia and colon tumor, is further studied by using the recently developed neural network-based finite impulse response extreme learning machine (FIR-ELM). It is seen that a time series analysis of the microarray samples is first performed to determine the filtering properties of the hidden layer of the neural classifier with FIR-ELM for feature identification. The linear separability of the data patterns in the microarray datasets is then studied. For improving the robustness of the neural classifier against noise and errors, a frequency domain gene feature selection algorithm is also proposed. It is shown in the simulation results that the FIR-ELM algorithm has an excellent performance for the classification of bioinformatics data in comparison with many existing classification algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a modified ELM algorithm that properly selects the input weights and biases before training the output weights of single-hidden layer feedforward neural networks with sigmoidal activation function and proves mathematically the hidden layer output matrix maintains full column rank. The modified ELM avoids the randomness compared with the ELM. The experimental results of both regression and classification problems show good performance of the modified ELM algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a new learning-based framework to jointly solve equalization and symbol detection problems in orthogonal frequency division multiplexing systems with quadrature amplitude modulation. The framework utilizes extreme learning machine (ELM), a recent addition to the class of supervised learning algorithms, to achieve fast training, high performance, and low error rates. The proposed ELM scheme employs infinitely differentiable nonlinear activation functions in least-square solution to learn the channel response, which is the equalization part. In addition to equalization, ELM performs symbol detection. Existing learning-based schemes require an additional symbol slicer for the symbol detection. The proposed framework does not experience training bottleneck imposed by gradient descent-based approaches. Simulation results show that the proposed framework outperforms other learning-based equalizers in terms of symbol error rate and training speeds. [ABSTRACT FROM AUTHOR]

As a novel learning algorithm for single-hidden-layer feedforward neural networks, extreme learning machines (ELMs) have been a promising tool for regression and classification applications. However, it is not trivial for ELMs to find the proper number of hidden neurons due to the nonoptimal input weights and hidden biases. In this paper, a new model selection method of ELM based on multi-objective optimization is proposed to obtain compact networks with good generalization ability. First, a new leave-one-out (LOO) error bound of ELM is derived, and it can be calculated with negligible computational cost once the ELM training is finished. Furthermore, the hidden nodes are added to the network one-by-one, and at each step, a multi-objective optimization algorithm is used to select optimal input weights by minimizing this LOO bound and the norm of output weight simultaneously in order to avoid over-fitting. Experiments on five UCI regression data sets are conducted, demonstrating that the proposed algorithm can generally obtain better generalization performance with more compact network than the conventional gradient-based back-propagation method, original ELM and evolutionary ELM. [ABSTRACT FROM AUTHOR]

Extreme learning machine (ELM) can be considered as a black-box modeling approach that seeks a model representation extracted from the training data. In this paper, a modified ELM algorithm, called symmetric ELM (S-ELM), is proposed by incorporating a priori information of symmetry. S-ELM is realized by transforming the original activation function of hidden neurons into a symmetric one with respect to the input variables of the samples. In theory, S-ELM can approximate N arbitrary distinct samples with zero error. Simulation results show that, in the applications where there exists the prior knowledge of symmetry, S-ELM can obtain better generalization performance, faster learning speed, and more compact network architecture. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extreme learning machine (ELM) with tunable activation function (TAF-ELM) learning algorithm, which determines its activation functions dynamically by means of the differential evolution algorithm based on the input data. The main objective is to overcome the problem dependence of fixed slop of the activation function in ELM. We mainly considered the issue of processing of benchmark problems on function approximation and pattern classification. Compared with ELM and E-ELM learning algorithms with the same network size or compact network configuration, the proposed algorithm has improved generalization performance with good accuracy. In addition, the proposed algorithm also has very good performance in the TAF neural networks learning algorithms. [ABSTRACT FROM AUTHOR]

In this paper, one geometrical topology hypothesis is present based on the optimal cognition principle, and the single-hidden layer feedforward neural network with extreme learning machine (ELM) is used for 3D object recognition. It is shown that the proposed approach can identify the inherent distribution and the dependence structure for each 3D object along multiple view angles by evaluating the local topological segments with a dipole topology model and developing the relevant mathematical criterion with ELM algorithm. The ELM ensemble is then used to combine the individual single-hidden layer feedforward neural network of each 3D object for performance improvements. The simulation results have shown the excellent performance and the effectiveness of the developed scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new classification method utilizing distance-based decision surface with nearest neighbor projection approach, called DDC. Kernel type of DDC has been extended to take into account the effective nonlinear structure of the data. DDC has some properties: (1) does not need conventional learning procedure (as k-NN algorithm), (2) does not need searching time to locate the k-nearest neighbors, and (3) does not need optimization process unlike some classification methods such as Support Vector Machine (SVM). In DDC, we compute the weighted average of distances to all the training samples. Unclassified sample will be classified as belonging to a class that has the minimum obtained distance. As a result, by such a rule we can derive a formula that can be used as the decision surface. DDC is tested on both synthetic and real-world data sets from the UCI repository, and the results were compared with k-NN, RBF Network, and SVM. The experimental results indicate DDC outperforms k-NN in the most experiments and the results are comparable to or better than SVM with some data sets. [ABSTRACT FROM AUTHOR]

To effectively handle speech data lying on a nonlinear manifold embedded in a high-dimensional acoustic space, in this paper, an adaptive supervised manifold learning algorithm based on locally linear embedding (LLE) for nonlinear dimensionality reduction is proposed to extract the low-dimensional embedded data representations for phoneme recognition. The proposed method aims to make the interclass dissimilarity maximized, while the intraclass dissimilarity minimized in order to promote the discriminating power and generalization ability of the low-dimensional embedded data representations. The performance of the proposed method is compared with five well-known dimensionality reduction methods, i.e., principal component analysis, linear discriminant analysis, isometric mapping (Isomap), LLE as well as the original supervised LLE. Experimental results on three benchmarking speech databases, i.e., the Deterding database, the DARPA TIMIT database, and the ISOLET E-set database, demonstrate that the proposed method obtains promising performance on the phoneme recognition task, outperforming the other used methods. [ABSTRACT FROM AUTHOR]

Prototype classifiers have been studied for many years. However, few methods can realize incremental learning. On the other hand, most prototype classifiers need users to predetermine the number of prototypes; an improper prototype number might undermine the classification performance. To deal with these issues, in the paper we propose an online supervised algorithm named Incremental Learning Vector Quantization (ILVQ) for classification tasks. The proposed method has three contributions. (1) By designing an insertion policy, ILVQ incrementally learns new prototypes, including both between-class incremental learning and within-class incremental learning. (2) By employing an adaptive threshold scheme, ILVQ automatically learns the number of prototypes needed for each class dynamically according to the distribution of training data. Therefore, unlike most current prototype classifiers, ILVQ needs no prior knowledge of the number of prototypes or their initial value. (3) A technique for removing useless prototypes is used to eliminate noise interrupted into the input data. Results of experiments show that the proposed ILVQ can accommodate the incremental data environment and provide good recognition performance and storage efficiency. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is a new machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one. However, when constructing the classification plane for one class, a large number of samples of this class are considered in the objective function, but only fewer samples in the other class are considered, which easily results in over-fitting problem. In addition, the same penalties are given to each misclassified samples in the TSVM. In fact, the misclassified samples have different effects on the decision of the hyper-plane. In order to overcome these two disadvantages, by introducing the rough set theory into ν-TSVM, we propose a rough margin-based ν-TSVM in this paper. In the proposed algorithm, the different points in the different positions are proposed to have different effects on the separating hyper-plane. We firstly construct rough lower margin, rough upper margin, and rough boundary in the ν-TSVM and then give the different penalties to the different misclassified samples according to their positions. The new classifier can avoid the over-fitting problem to a certain extent. Numerical experiments on one artificial dataset and six benchmark datasets demonstrate the feasibility and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The harmony search (HS) method is a popular meta-heuristic optimization algorithm, which has been extensively employed to handle various engineering problems. However, it sometimes fails to offer a satisfactory convergence performance under certain circumstances. In this paper, we propose and study a hybrid HS approach, HS-PBIL, by merging the HS together with the population-based incremental learning (PBIL). Numerical simulations demonstrate that our HS-PBIL is well capable of outperforming the regular HS method in dealing with nonlinear function optimization and a practical wind generator optimization problem. [ABSTRACT FROM AUTHOR]

Ensemble learning has gained considerable attention in different learning tasks including regression, classification, and clustering problems. One of the drawbacks of the ensemble is the high computational cost of training stages. Resampling local negative correlation (RLNC) is a technique that combines two well-known methods to generate ensemble diversity-resampling and error negative correlation-and a fine-grain parallel approach that allows us to achieve a satisfactory balance between accuracy and efficiency. In this paper, we introduce a structure of the virtual machine aimed to test diverse selection strategies of parameters in neural ensemble designs, such as RLNC. We assess the parallel performance of this approach on a virtual machine cluster based on the full virtualization paradigm, using speedup and efficiency as performance metrics, for different numbers of processors and training data sizes. [ABSTRACT FROM AUTHOR]

In this paper, we present nonmonotone variants of the Levenberg-Marquardt (LM) method for training recurrent neural networks (RNNs). These methods inherit the benefits of previously developed LM with momentum algorithms and are equipped with nonmonotone criteria, allowing temporal increase in training errors, and an adaptive scheme for tuning the size of the nonmonotone slide window. The proposed algorithms are applied to training RNNs of various sizes and architectures in symbolic sequence-processing problems. Experiments show that the proposed nonmonotone learning algorithms train more effectively RNNs for sequence processing than the original monotone methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel steam valving controller using radial basis function (RBF) networks-based approximate model method. Approximate model method is a kind of direct linearization approach that is derived based on the approximation of the plant's input-output model via Taylor expansion. RBF networks are used to identify the plant to implement the approximate model control law. In order to improve the performance of the approximate model controller, RBF networks weights are adjusted online using BP algorithms with an adaptive learning rate. Several simulations results demonstrate the effectiveness of the proposed controller for team valving control. [ABSTRACT FROM AUTHOR]

The Support Vector Machine (SVM) is an interesting classifier with excellent power of generalization. In this paper, we consider applying the SVM to semi-supervised learning. We propose using an additional criterion with the standard formulation of the semi-supervised SVM ( S VM) to reinforce classifier regularization. Since, we deal with nonconvex and combinatorial problem, we use a genetic algorithm to optimize the objective function. Furthermore, we design the specific genetic operators and certain heuristics in order to improve the optimization task. We tested our algorithm on both artificial and real data and found that it gives promising results in comparison with classical optimization techniques proposed in literature. [ABSTRACT FROM AUTHOR]

This paper presents a new method for fault classification in series-compensated transmission line using multiclass support vector machine (MCSVM) and multi class extreme learning machine (MCELM). These methods use the information obtained from the wavelet decomposition of fault current signals for fault classification. Using MATLAB simulink, data set has been generated with different types of fault and system variables, which include the fault resistance, fault distance, load angle and fault inception angle. The proposed method has been tested on a 400-kV, 300-km transmission line under variety of fault conditions. The performance of MCSVM and MCELM is compared in terms of training time and classification accuracy. The comparisons have been made for both One-Versus-One and One-Versus-Rest methods of SVMs and ELMs. Results show that MCELMs need less training time compared to MCSVMs, and the classification accuracy of MCELMs is more or less similar to MCSVMs. The feasibility of the proposed methods is also tested on a practical 220-kV series-compensated transmission line, and the results obtained are quite promising. [ABSTRACT FROM AUTHOR]

This paper deals with the parallel layer perceptron (PLP) complexity control, bias and variance dilemma, using a multiobjective (MOBJ) training algorithm. To control the bias and variance the training process is rewritten as a bi-objective problem, considering the minimization of both training error and norm of the weight vector, which is a measure of the network complexity. This method is applied to regression and classification problems and compared with several other training procedures and topologies. The results show that the PLP MOBJ training algorithm presents good generalization results, outperforming traditional methods in the tested examples. [ABSTRACT FROM AUTHOR]