On sharpness of error bounds for multivariate neural network approximation

Multilayer perceptrons with hard-limiting (signum) activation functions can form complex decision regions. It is well known that a three-layer perceptron (two hidden layers) can form arbitrary disjoint decision regions and a two-layer perceptron (one hidden layer) can form single convex decision regions. This paper further proves that single hidden layer feedforward neural networks (SLFN's) with any continuous bounded nonconstant activation function or any arbitrary bounded (continuous or not continuous) activation function which has unequal limits at infinities (not just perceptrons) can form disjoint decision regions with arbitrary shapes in multidimensional cases. SLFN's with some unbounded activation function can also form disjoint decision regions with arbitrary shapes.

The two-dimensional morphology of the cladding layer has an important influence on the quality of the cladding layer and the crack tendency. Using the powerful nonlinear processing ability of the single hidden layer feedforward neural network, a prediction model between the cladding technological parameters and the two-dimensional morphology of the cladding layer is established. Taking the cladding parameters as the input and the two-dimensional morphology of the cladding as the output, the experimental data is used to train the network to achieve a high-level mapping of the input and output. On this basis, the algorithm of extreme learning machine is used to optimize the single hidden layer feedforward neural network to overcome the problems of slow convergence speed, more network training parameters and easy local convergence in back-propagation algorithm. The results show that the relationship between the cladding process parameters and the two-dimensional morphology of the cladding layer can be roughly reflected by the back-propagation algorithm. However, the prediction results are not stable and the error rate is between 10% and 40%. The neural network optimized by the extreme learning machine is utilized to get a better prediction result. The error rate is 10–20%.

The single hidden layer feed-forward neural networks has simple structure, good approximation performance on real applications. The on-line learning algorithms based on the single hidden layer feed-forward neural networks have the ability of real time on-line learning and are suitable to sequential learning environments and applications. The sunspot number prediction is an important content in the space environment forecast. According to the strong nonlinear characteristics and difficult mid long term prediction problem for sunspot, an improved on-line extreme learning machine with good approximation ability and generation performance is applied to sunspot number chaotic time series prediction in this paper, The improved algorithm updates the output-layer weights with a Givens QR decomposition based on the orthogonalized least squares algorithm. Simulation results show that the improved algorithm can avoid the singular of the hidden layer output matrix and obtain better network performance. The improved algorithm provides a comparing fast and real time on-line learning ability for sunspot chaotic time series space environmental prediction.

An alternative modeling technique of vehicle suspension system which is based on an integration between wavelet theory and artificial neural network, or wavelet network (wavenet) is presented. Wavenet is a single hidden layer feedforward neural network, which uses wavelet basis function as an activation function. Polynomial windowed with Gaussian (POLYWOG) will be applied as the basis function. Wavenet parameters, such as weight, dilation and translation of the wavelet function will be optimized during its learning process, which is performed by a backpropagation algorithm. For minimizing the mean square error between model outputs and its observation, an iterative minimization method of gradient steepest descent is applied. Experimental evaluation of the proposed technique has been conducted using an input-output data collected from a running test vehicle. Observations by comparing the model responses with the actual output measurements revealed that satisfactory model matching were obtained which means that the models have captured the real basic features of the vehicle suspension dynamic characteristics

A recent paper addresses a certain classification problem, and concludes that classification can be achieved using a single hidden layer neural network. We note here that conclusions along similar lines in a more general setting were reached in an earlier paper.

This chapter describes some/new artificial neural network (ANN) neuromodeling techniques and natural optimization algorithms for electromagnetic modeling and optimization of nonlinear devices and circuits. Neuromodeling techniques presented are based on single hidden layer feedforward neural network configurations, which are trained by the resilient back-propagation algorithm to solve the modeling learning tasks associated with device or circuit under analysis. Modular configurations of these feedforward networks and optimal neural networks are also presented considering new activation functions for artificial neurons. In addition, some natural optimization algorithms are described, such as continuous genetic algorithm (GA), a proposed improved-GA and particle swarm optimization (PSO). These natural optimization algorithms are blended with multilayer perceptrons (MLP) artificial neural network models for fast and accurate resolution of optimization problems. Some examples of applications are presented and include nonlinear RF/microwave devices and circuits, such as transistors, filters and antennas.

COVID-19 is a disease or virus that has recently spread worldwide. The disease has also taken many casualties because the virus is notoriously deadly. An examination can be carried out using a chest X-Ray because it costs cheaper compared to swab and PCR tests. The data used in this study was chest X-Ray image data. Chest X-Ray images can be identified using Computer-Aided Diagnosis by utilizing machine learning classification. The first step was the preprocessing stage and feature extraction using the Gray Level Co-Occurrence Matrix (GLCM). The result of the feature extraction was then used at the classification stage. The classification process used was Extreme Learning Machine (ELM). Extreme Learning Machine (ELM) is one of the artificial neural networks with advanced feedforward which has one hidden layer called Single Hidden Layer Feedforward Neural Networks (SLFNs). The results obtained by GLCM feature extraction and classification using ELM achieved the best accuracy of 91.21%, the sensitivity of 100%, and the specificity of 91% at 135° rotation using linear activation function with 15 hidden nodes.

A test suite plays a key role in software testing. Mutation testing is a powerful approach to measure the fault-detection ability of a test suite. The mutation testing process requires a large number of mutants to be generated and executed. Hence, mutation testing is also computationally expensive. To solve this problem, predictive mutation testing builds a classification model to predict the test result of each mutant. However, the existing predictive mutation testing methods only can be used to estimate the overall mutation scores of object-oriented programs. To overcome the shortcomings of the existing methods, we propose a new method to directly predict the mutation score for each statement in process-oriented programs. Compared with the existing predictive mutation testing methods, our method uses more dynamic program execution features, which more adequately reflect dynamic dependency relationships among the statements and more accurately reflects information propagation during the execution of test cases. By comparing the prediction effects of logistic regression, artificial neural network, random forest, support vector machine, and symbolic regression, we finally decide to use a single hidden layer feedforward neural network as the predictive model to predict the statement mutation scores. In our two experiments, the mean absolute errors between the statement mutation scores predicted by the neural network and the real statement mutation scores both approximately reach 0.12.

In this paper tomographic reconstruction based on the concept of ridge functions (Logan and Shepp) is considered. A reconstruction approach for the ridge functions from a finite number of arbitrary projections is suggested within the framework of parallel beam geometry. The method deals with images that can be presented as a sum of ridge functions. This assumption results in a consistent linear system of Fredholm integral equations of the third kind in terms of one-dimensional functions. We derive a formula to calculate the ridge functions from the set of arbitrary projections. In the case of equally spaced projections formulae for the analytical inversion of matrices encountered in the calculation of ridge functions are derived.

Letter: On non-iterative learning algorithms with closed-form solution

This paper proposes a novel artificial neural network called Parallel Layer Perceptron Fast Learning Network (PLP-FLN). In PLP-FLN, a parallel single hidden layer feed-forward neural network is added on the basis of Fast Learning Network (FLN) which is an improved Extreme Learning Machine (ELM). Input weights and hidden layer biases are randomly generated. The weights connect the output nodes and the input nodes, and the weights connect the output nodes and the hidden nodes are analytically determined based on least squares methods. In order to test the PLP-FLN validity, this paper compared it with ELM, FLN, Kernel ELM and Incremental ELM through 12 regression applications and 7 classification problems. By comparing the experimental results, it shows that the PLP-FLN with much more compact networks have demonstrated better approximations, classification performances and generalization ability.

Extreme learning machine is a novel single hidden layer feedforward neural networks with a strong abilities, for example simple net structure, fast learning speed, good generalization and so on. Aimed at the system with a delay unit, A new control strategy for internal model control is proposed to set up an inverse model of the minimal phase subsystem by using extreme learning machine with in-out system datum. Moreover, the relative stable error for internal model control system with a delay unit is presented to evaluate the system performance. The features for the internal model control system based on extreme learning machine are compared with that based on neural network. The experimental results indicate that the internal model control system based on extreme learning machine has small stable error and strong robustness.

Extreme Learning Machine (ELM) is a single hidden layer feed-forward neural network learning method, which has a high generalization performance as well as faster. In this paper, odour data is discriminated based on the sensor response curve by using ELM, and the main objective is to investigate the optimum number of nodes in the hidden layer of ELM for olfactory detection. The relationship between the number of nodes in the hidden layer and the number of attributes or classes of dataset is queried to achieve the goal. Three odour datasets taken from different sources in literature and two transfer functions for the ELM are used to verify the results of the study. The backpropagation (BP) algorithm is also used for training an artificial neural network for comparison purposes. The analysis is performed for the three datasets by using ELM and BP and obtained results present that the time consumption of ELM is too small to be compared with BP even though the number of nodes is high and better accuracy rates are obtained by ELM.

The main objective of this works is to study and improve the performances of the Single hidden Layer Feedforward Neural network (SLFN) for the application of Remaining Useful Life (RUL) prediction of aircraft engines. The most common problems in SLFNs based old training algorithms such as backpropagation are time consuming, over-fitting and the appropriate network architecture identification. In this paper a new incremental constructive learning algorithm based on Extreme Learning Machine algorithm is proposed for founding the appropriate architecture of a neural network under less computational costs. The aim of the proposed training approach is to study its maximum capabilities during RUL prediction by reducing over-fitting and human intervention. The performances of the proposed approach which are evaluated on C-MAPPS dataset and compared with its original variant from the literature. Experimental results proved that the new algorithm outperforms the old one in many metrics evaluations.

This dissertation studies a class of evolving neural networks for system modeling from data streams. The class encompasses single hidden layer feedforward neural networks with variable and online definition of the number of hidden neurons.