Approximation results for neural network operators activated by sigmoidal functions

Costarelli, Danilo; Spigler, Renato

doi:10.1016/j.neunet.2013.03.015

Cited by 146 publications

(73 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Before training on STSM6080I NDPD from TS (2), 2LP (6) ( 1 5 ) is initialized with MATLAB function "feedforwardnet" from the Neural Network Toolbox [4], [9], [13] Such a transfer within the Neural Network Toolbox is implemented with logarithmic sigmoid MATLAB transfer function "logsig" , which has the derivative due to its smooth "S-shape" [7], [16], [17]. Then 2LP (15) , (16) having been adapted with weight and bias learning rules by Neural Network Toolbox adapt function "adaptwb", is going to be trained with MATLAB backpropagation training function "traingda" (see its usage in [3], [4], [7], [9], [12], [18], [19]). Function "traingda" will update 4800 300 300 26 300 26 1 448 126…”

Section: Description Of 2lp (6) Configuration For M6080ismentioning

confidence: 99%

Classifying Scaled-Turned-Shifted Objects with Optimal Pixel-to-Scale-Turn-Shift Standard Deviations Ratio in Training 2-Layer Perceptron on Scaled-Turned-Shifted 4800-Featured Objects under Normally Distributed Feature Distortion

Romanuke

2017

Electrical, Control and Communication Engineering

View full text Add to dashboard Cite

-The problem of classifying diversely distorted objects is considered. The classifier is a 2-layer perceptron capable of classifying greater amounts of objects in a unit of time. This is an advantage of the 2-layer perceptron over more complex neural networks like the neocognitron, the convolutional neural network, and the deep learning neural networks. Distortion types are scaling, turning, and shifting. The object model is a monochrome 60 × 80 image of the enlarged English alphabet capital letter. Consequently, there are 26 classes of 4800-featured objects. Training sets have a parameter, which is the ratio of the pixel-to-scale-turn-shift standard deviations, which allows controlling normally distributed feature distortion. An optimal ratio is found, at which the performance of the 2-layer perceptron is still unsatisfactory. Then, the best classifier is further trained with additional 438 passes of training sets by increasing the training smoothness tenfold. This aids in decreasing the ultimate classification error percentage from 35.23 % down to 12.92 %. However, the expected practicable distortions are smaller, so the percentage corresponding to them becomes just 1.64 %, which means that only one object out of 61 is misclassified. Such a solution scheme is directly applied to other classification problems, where the number of features is a thousand or a few thousands by a few tens of classes.

show abstract

Section: Description Of 2lp (6) Configuration For M6080ismentioning

confidence: 99%

Classifying Scaled-Turned-Shifted Objects with Optimal Pixel-to-Scale-Turn-Shift Standard Deviations Ratio in Training 2-Layer Perceptron on Scaled-Turned-Shifted 4800-Featured Objects under Normally Distributed Feature Distortion

Romanuke

2017

Electrical, Control and Communication Engineering

View full text Add to dashboard Cite

show abstract

“…Logistic functions are often used in artificial neural networks [5], [16], [17], [23]. Any neural net element computes a linear combination of its input signals, and applies a logistic function to the result; often called "activation" function.…”

Section: Preliminariesmentioning

confidence: 99%

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Илиев

Kyurkchiev²,

Markov³

2015

BIOMATH

View full text Add to dashboard Cite

Abstract-We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued step function is discussed using Hausdorff metric. Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

show abstract

“…1. The relaxation function (25) whose values are a multiplier factor to the temporary CEP. They show how the current CEP may increase so that this increment would be counted insignificant, and when inequality (24) is false we could accept 2LP   * q N P after the q -th pass as the temporary one.…”

Section: Solutionmentioning

confidence: 99%

Optimal Training Parameters and Hidden Layer Neuron Number of Two-Layer Perceptron for Generalised Scaled Object Classification Problem

Romanuke

2015

Information Technology and Management Science

View full text Add to dashboard Cite

-The research is focused on optimising two-layer perceptron for generalised scaled object classification problem. The optimisation criterion is minimisation of inaccuracy. The inaccuracy depends on training parameters and hidden layer neuron number. After its statistics is accumulated, minimisation is executed by a numerical search. Perceptron is optimised additionally by extra training. As it is done, the classification error percentage does not exceed 3 % in case of the worst scale distortion.

show abstract

Approximation results for neural network operators activated by sigmoidal functions

Cited by 146 publications

References 24 publications

Classifying Scaled-Turned-Shifted Objects with Optimal Pixel-to-Scale-Turn-Shift Standard Deviations Ratio in Training 2-Layer Perceptron on Scaled-Turned-Shifted 4800-Featured Objects under Normally Distributed Feature Distortion

Classifying Scaled-Turned-Shifted Objects with Optimal Pixel-to-Scale-Turn-Shift Standard Deviations Ratio in Training 2-Layer Perceptron on Scaled-Turned-Shifted 4800-Featured Objects under Normally Distributed Feature Distortion

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Optimal Training Parameters and Hidden Layer Neuron Number of Two-Layer Perceptron for Generalised Scaled Object Classification Problem

Contact Info

Product

Resources

About