scholarly journals Asymptotic Expansion for Neural Network Operators of the Kantorovich Type and High Order of Approximation

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Marco Cantarini ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Neural Network ◽  
Asymptotic Expansion ◽  
Type Theorem ◽  
Activation Function ◽  
Pointwise Approximation ◽  
Linear Combinations ◽  
Voronovskaja Type Theorem ◽  
Sigmoidal Functions ◽  
The Neural Network ◽  
Finite Linear

AbstractIn this paper, we study the rate of pointwise approximation for the neural network operators of the Kantorovich type. This result is obtained proving a certain asymptotic expansion for the above operators and then by establishing a Voronovskaja type formula. A central role in the above resuts is played by the truncated algebraic moments of the density functions generated by suitable sigmoidal functions. Furthermore, to improve the rate of convergence, we consider finite linear combinations of the above neural network type operators, and also in the latter case, we obtain a Voronovskaja type theorem. Finally, concrete examples of sigmoidal activation functions have been deeply discussed, together with the case of rectified linear unit (ReLu) activation function, very used in connection with deep neural networks.

SCORING MODELING BASED ON NEURAL NETWORKS FOR DETERMINING A BANK BORROWER'S RATING

2020 ◽  
Vol 2020 (10) ◽  
pp. 54-62
Author(s):  
Oleksii VASYLIEV ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Statistical Data ◽  
Activation Function ◽  
Decision Making Process ◽  
Neural Network Architecture ◽  
Acceptable Accuracy ◽  
The Neural Network ◽  
Sigmoid Activation Function

The problem of applying neural networks to calculate ratings used in banking in the decision-making process on granting or not granting loans to borrowers is considered. The task is to determine the rating function of the borrower based on a set of statistical data on the effectiveness of loans provided by the bank. When constructing a regression model to calculate the rating function, it is necessary to know its general form. If so, the task is to calculate the parameters that are included in the expression for the rating function. In contrast to this approach, in the case of using neural networks, there is no need to specify the general form for the rating function. Instead, certain neural network architecture is chosen and parameters are calculated for it on the basis of statistical data. Importantly, the same neural network architecture can be used to process different sets of statistical data. The disadvantages of using neural networks include the need to calculate a large number of parameters. There is also no universal algorithm that would determine the optimal neural network architecture. As an example of the use of neural networks to determine the borrower's rating, a model system is considered, in which the borrower's rating is determined by a known non-analytical rating function. A neural network with two inner layers, which contain, respectively, three and two neurons and have a sigmoid activation function, is used for modeling. It is shown that the use of the neural network allows restoring the borrower's rating function with quite acceptable accuracy.

Analysis of Fin-Tube Evaporator Performance With Limited Experimental Data Using Artificial Neural Networks

2000 ◽  
Author(s):  
Arturo Pacheco-Vega ◽  
Mihir Sen ◽  
Rodney L. McClain
Keyword(s):  
Neural Network ◽  
Heat Rate ◽  
Network Models ◽  
Activation Function ◽  
Operating Conditions ◽  
Training Data ◽  
Neural Network Models ◽  
The Neural Network ◽  
Artificial Neural ◽  
Fin Tube

Abstract In the current study we consider the problem of accuracy in heat rate estimations from artificial neural network models of heat exchangers used for refrigeration applications. The network configuration is of the feedforward type with a sigmoid activation function and a backpropagation algorithm. Limited experimental measurements from a manufacturer are used to show the capability of the neural network technique in modeling the heat transfer in these systems. Results from this exercise show that a well-trained network correlates the data with errors of the same order as the uncertainty of the measurements. It is also shown that the number and distribution of the training data are linked to the performance of the network when estimating the heat rates under different operating conditions, and that networks trained from few tests may give large errors. A methodology based on the cross-validation technique is presented to find regions where not enough data are available to construct a reliable neural network. The results from three tests show that the proposed methodology gives an upper bound of the estimated error in the heat rates.

Signal processing algorithm for neural networks with integrodifferential splines as an activation function and its particular case of image classification

2021 ◽  
Author(s):  
T.K. Biryukova
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Image Classification ◽  
Activation Function ◽  
Experimental Comparison ◽  
Training Time ◽  
Operation Speed ◽  
The Neural Network ◽  
Linear Algebraic Equations ◽  
Network Operation

Classic neural networks suppose trainable parameters to include just weights of neurons. This paper proposes parabolic integrodifferential splines (ID-splines), developed by author, as a new kind of activation function (AF) for neural networks, where ID-splines coefficients are also trainable parameters. Parameters of ID-spline AF together with weights of neurons are vary during the training in order to minimize the loss function thus reducing the training time and increasing the operation speed of the neural network. The newly developed algorithm enables software implementation of the ID-spline AF as a tool for neural networks construction, training and operation. It is proposed to use the same ID-spline AF for neurons in the same layer, but different for different layers. In this case, the parameters of the ID-spline AF for a particular layer change during the training process independently of the activation functions (AFs) of other network layers. In order to comply with the continuity condition for the derivative of the parabolic ID-spline on the interval (x x0, n) , its parameters fi (i= 0,...,n) should be calculated using the tridiagonal system of linear algebraic equations: To solve the system it is necessary to use two more equations arising from the boundary conditions for specific problems. For exam- ple the values of the grid function (if they are known) in the points (x x0, n) may be used for solving the system above: f f x0 = ( 0) , f f xn = ( n) . The parameters Iii+1 (i= 0,...,n−1 ) are used as trainable parameters of neural networks. The grid boundaries and spacing of the nodes of ID-spline AF are best chosen experimentally. The optimal selection of grid nodes allows improving the quality of results produced by the neural network. The formula for a parabolic ID-spline is such that the complexity of the calculations does not depend on whether the grid of nodes is uniform or non-uniform. An experimental comparison of the results of image classification from the popular FashionMNIST dataset by convolutional neural 0, x< 0 networks with the ID-spline AFs and the well-known ReLUx( ) =AF was carried out. The results reveal that the usage x x, ≥ 0 of the ID-spline AFs provides better accuracy of neural network operation than the ReLU AF. The training time for two convolutional layers network with two ID-spline AFs is just about 2 times longer than with two instances of ReLU AF. Doubling of the training time due to complexity of the ID-spline formula is the acceptable price for significantly better accuracy of the network. Wherein the difference of an operation speed of the networks with ID-spline and ReLU AFs will be negligible. The use of trainable ID-spline AFs makes it possible to simplify the architecture of neural networks without losing their efficiency. The modification of the well-known neural networks (ResNet etc.) by replacing traditional AFs with ID-spline AFs is a promising approach to increase the neural network operation accuracy. In a majority of cases, such a substitution does not require to train the network from scratch because it allows to use pre-trained on large datasets neuron weights supplied by standard software libraries for neural network construction thus substantially shortening training time.

Smartphone Based Classification System for Indoor Navigation

2015 ◽  
Vol 775 ◽  
pp. 436-440
Author(s):  
Yazan Aljeroudi ◽  
Ari Legowo ◽  
Erwin Sulaeman
Keyword(s):  
Neural Network ◽  
Classification System ◽  
Indoor Environment ◽  
Activation Function ◽  
Indoor Navigation ◽  
The Neural Network ◽  
Evaluation Measure ◽  
Tuning Process ◽  
Learning Machine ◽  
Accuracy Rates

This paper introduces a smartphone-based classification system for an indoor environment of a walking person. The system relies only on smartphone inertial data and it can be considered as a smartphone-based aiding system for an indoor navigation. In addition, it does not need pre-installing of wireless network in the environment or heavily tuning process before the navigation run. Therefore, this system can be used as an aiding block where the person wants to localize himself in an indoor environment starting from known navigations point. This system categorizes person navigation in indoor environment into three types of classes: walking straight, turning right, and turning left. There is an ELM (Extreme Learning Machine)-Based neural network for deciding the class of the current navigation action. The evaluation measure shows that the best performance is obtained with the Radial Basis Function (RBF) as the activation function of the neural network. Also, the obtained accuracy rates up to 95%.

Prediction of stress in fillet portion of spur gears using artificial neural networks

2007 ◽  
Vol 22 (1) ◽  
pp. 41-51
Author(s):  
M.S. Shunmugam ◽  
N. Siva Prasad
Keyword(s):  
Neural Network ◽  
Gear Tooth ◽  
Spur Gear ◽  
Activation Function ◽  
Training Data ◽  
Spur Gears ◽  
Pressure Angle ◽  
The Neural Network ◽  
Artificial Neural ◽  
Taguchi’S Design Of Experiments

AbstractA fillet curve is provided at the root of the spur gear tooth, as stresses are high in this portion. The fillet curve may be a trochoid or an arc of suitable size as specified by designer. The fillet stress is influenced by the fillet geometry as well as the number of teeth, modules, and the pressure angle of the gear. Because the relationship is nonlinear and complex, an artificial neural network and a backpropagation algorithm are used in the present work to predict the fillet stresses. Training data are obtained from finite element simulations that are greatly reduced using Taguchi's design of experiments. Each simulation takes around 30 min. The 4-5-1 network and a sigmoid activation function are chosen. TRAINLM function is used for training the network with a learning rate parameter of 0.01 and a momentum constant of 0.8. The neural network is able to predict the fillet stresses in 0.03 s with reasonable accuracy for spur gears having 25–125 teeth, a 1–5 mm module, a 0.05–0.45 mm fillet radius, and a 15°–25° pressure angle.

scholarly journals The Construction and Approximation of the Neural Network with Two Weights

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiyong Quan ◽  
Zhengqiu Zhang
Keyword(s):  
Neural Network ◽  
Fourier Series ◽  
Continuous Function ◽  
Bp Neural Network ◽  
Partition Of Unity ◽  
Sigmoidal Functions ◽  
The Neural Network ◽  
Inequality Technique ◽  
The Way

The technique of approximate partition of unity, the way of Fourier series, and inequality technique are used to construct a neural network with two weights and with sigmoidal functions. Furthermore by using inequality technique, we prove that the neural network with two weights can more precisely approximate any nonlinear continuous function than BP neural network constructed in (Chen et al., 2012).

scholarly journals Neural Network Based of a New User IP Address Determination and Address Conflict Elimination

2019 ◽  
Vol 12 (3) ◽  
pp. 15-22
Author(s):  
Raid W. Daoud
Keyword(s):  
Neural Network ◽  
Work Performance ◽  
Activation Function ◽  
Training Process ◽  
Security Issue ◽  
Ip Address ◽  
The Neural Network ◽  
The Given ◽  
User Device ◽  
Good Manner

In this paper, the neural network (NN) is used to control the remote IP address that related to user device. When the IP address assigned carefully and controlled by a novel tool, the work performance and service quality will be better. The input for the NN determined depending on the repeated problem in recent networks and the available parameters which are in the main server node. The training process done by determining the required training function and activation function for all neurons in the NN. The performance of the proposed method was (1*10-20) or less in more cases and the error of the learning process is nearly (1*10-6). In addition to IP address control, the proposed method is a good manner to optimize the security issue by specializing an IP address for a given user that can't be used by other device. Finally, the NN subject the produced IP address for the given users for test and validation which reached to the goal at smallest time (~0.0001s) and little number of iteration (9 - 20) epoch.

scholarly journals A Compound Controller of an Aerial Manipulator Based on Maxout Fuzzy Neural Network

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xinchen Qi ◽  
Jianwei Wu ◽  
Jiansheng Pan
Keyword(s):  
Neural Network ◽  
Fuzzy Neural Network ◽  
Fuzzy Theory ◽  
Activation Function ◽  
Attitude Error ◽  
The Neural Network ◽  
Aerial Manipulator ◽  
Fuzzy Neural ◽  
Neural Network Algorithm ◽  
The Stability

The aerial manipulator is a complex system with high coupling and instability. The motion of the robotic arm will affect the self-stabilizing accuracy of the unmanned aerial vehicles (UAVs). To enhance the stability of the aerial manipulator, a composite controller combining conventional proportion integration differentiation (PID) control, fuzzy theory, and neural network algorithm is proposed. By blurring the attitude error signal of UAV as the input of the neural network, the anti-interference ability and stability of UAV is improved. At the same time, a neural network model identifier based on Maxout activation function is built to realize accurate recognition of the controlled model. The simulation results show that, compared with the conventional PID controller, the composite controller combined with fuzzy neural network can improve the anti-interference ability and stability of UAV greatly.

scholarly journals Early Dropout Prediction Model: A Case Study of University Leveling Course Students

2020 ◽  
Vol 12 (22) ◽  
pp. 9314 ◽  
Author(s):  
Iván Sandoval-Palis ◽  
David Naranjo ◽  
Jack Vidal ◽  
Raquel Gilar-Corbi
Keyword(s):  
Neural Network ◽  
Early Stage ◽  
Activation Function ◽  
Dropping Out ◽  
Student Dropout ◽  
The Neural Network ◽  
Early Dropout ◽  
Substantial Investment ◽  
University Dropout ◽  
National Governments

The school-dropout problem is a serious issue that affects both a country’s education system and its economy, given the substantial investment in education made by national governments. One strategy for counteracting the problem at an early stage is to identify students at risk of dropping out. The present study introduces a model to predict student dropout rates in the Escuela Politécnica Nacional leveling course. Data related to 2097 higher education students were analyzed; a logistic regression model and an artificial neural network model were trained using four variables, which incorporated student academic and socio-economic information. After comparing the two models, the neural network, with an experimentally defined architecture of 4–7–1 architecture and a logistic activation function, was selected as the model that should be applied to early predict dropout in the leveling course. The study findings show that students with the highest risk of dropping out are those in vulnerable situations, with low application grades, from the Costa regime, who are enrolled in the leveling course for technical degrees. This model can be used by the university authorities to identify possible dropout cases, as well as to establish policies to reduce university dropout and failure rates.

Prediction of Humid Air Heat Exchanger Performance Using Artificial Neural Networks

1999 ◽  
Author(s):  
Arturo Pacheco-Vega ◽  
Mihir Sen ◽  
K. T. Yang ◽  
Rodney L. McClain
Keyword(s):  
Neural Network ◽  
Heat Exchanger ◽  
Activation Function ◽  
Humid Air ◽  
The Neural Network ◽  
Artificial Neural ◽  
Fin Tube ◽  
Experimental Values ◽  
Sigmoid Activation Function ◽  
Better Than

Abstract In the present study we apply an artificial neural network to predict the operation of a humid air-water fin-tube compact heat exchanger. The network configuration is of the feedforward type with a sigmoid activation function and a backpropagation algorithm. Published experimental data, corresponding to humid air flowing over the heat exchanger tubes and water flowing inside them, are used to train the neural network. After training with known experimental values of the humid-air flow rates, dry-bulb and wet-bulb inlet temperatures for various geometrical configurations, the j-factor and heat transfer rate predictions of the network were tested against the experimental values. Comparisons were made with published predictions of power-law correlations which were obtained from the same data. The results demonstrate that the neural network is able to predict the performance of this heat exchanger much better than the correlations.

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