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This article presents a novel representation of artificial neural networks (ANNs) that is based on a projection of weights into a new spherical space defined by a radius $r$ and a vector of angles $\Theta $. This spherical representation of ANNs further simplifies the multiobjective learning problem, which is usually treated as a constrained optimization problem that requires great computational effort to maintain the constraints. With the proposed spherical representation, the constrained optimization problem becomes unconstrained, which simplifies the formulation and computational effort required. In addition, it also allows the use of any nonlinear optimization method for the multiobjective learning of ANNs. Results presented in this article show that the proposed spherical representation of weights yields more accurate estimates of the Pareto set than the classical multiobjective approach. Regarding the final solution selected from the Pareto set, our approach was effective and outperformed some state-of-the-art methods on several data sets. [ABSTRACT FROM AUTHOR]

In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, and for a class of MLPs whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The increasing liberalization of European electricity markets, the growing proportion of intermittent renewable energy being fed into the energy grids, and also new challenges in the patterns of energy consumption (such as electric mobility) require flexible and intelligent power grids capable of providing efficient, reliable, economical, and sustainable energy production and distribution. From the supplier side, particularly, the integration of renewable energy sources (e.g., wind and solar) into the grid imposes an engineering and economic challenge because of the limited ability to control and dispatch these energy sources due to their intermittent characteristics. Time-series prediction of wind speed for wind power production is a particularly important and challenging task, wherein prediction intervals (PIs) are preferable results of the prediction, rather than point estimates, because they provide information on the confidence in the prediction. In this paper, two different machine learning approaches to assess PIs of time-series predictions are considered and compared: 1) multilayer perceptron neural networks trained with a multiobjective genetic algorithm and 2) extreme learning machines combined with the nearest neighbors approach. The proposed approaches are applied for short-term wind speed prediction from a real data set of hourly wind speed measurements for the region of Regina in Saskatchewan, Canada. Both approaches demonstrate good prediction precision and provide complementary advantages with respect to different evaluation criteria. [ABSTRACT FROM PUBLISHER]

Extreme learning machine (ELM) is an emerging learning algorithm for the generalized single hidden layer feedforward neural networks, of which the hidden node parameters are randomly generated and the output weights are analytically computed. However, due to its shallow architecture, feature learning using ELM may not be effective for natural signals (e.g., images/videos), even with a large number of hidden nodes. To address this issue, in this paper, a new ELM-based hierarchical learning framework is proposed for multilayer perceptron. The proposed architecture is divided into two main components: 1) self-taught feature extraction followed by supervised feature classification and 2) they are bridged by random initialized hidden weights. The novelties of this paper are as follows: 1) unsupervised multilayer encoding is conducted for feature extraction, and an ELM-based sparse autoencoder is developed via \ell 1 constraint. By doing so, it achieves more compact and meaningful feature representations than the original ELM; 2) by exploiting the advantages of ELM random feature mapping, the hierarchically encoded outputs are randomly projected before final decision making, which leads to a better generalization with faster learning speed; and 3) unlike the greedy layerwise training of deep learning (DL), the hidden layers of the proposed framework are trained in a forward manner. Once the previous layer is established, the weights of the current layer are fixed without fine-tuning. Therefore, it has much better learning efficiency than the DL. Extensive experiments on various widely used classification data sets show that the proposed algorithm achieves better and faster convergence than the existing state-of-the-art hierarchical learning methods. Furthermore, multiple applications in computer vision further confirm the generality and capability of the proposed learning scheme. [ABSTRACT FROM AUTHOR]

Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN. [ABSTRACT FROM AUTHOR]