Approximation by network operators with logistic activation functions

Chen, Zhixiang; Cao, Feilong; Hu, Jinjie

doi:10.1016/j.amc.2015.01.049

Cited by 14 publications

(12 citation statements)

References 23 publications

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“…A CNN architecture is formed by a stack of distinct layers that transform the input volume into the output volume. The transformation is executed through differentiable functions [5]- [7]. The output holds scores of the classes [8]- [10].…”

Section: An Open Problem Of Setting Hyperparametersmentioning

confidence: 99%

Smooth Non-increasing Square Spatial Extents of Filters in Convolutional Layers of CNNs for Image Classification Problems

Romanuke

2018

Applied Computer Systems

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The present paper considers an open problem of setting hyperparameters for convolutional neural networks aimed at image classification. Since selecting filter spatial extents for convolutional layers is a topical problem, it is approximately solved by accumulating statistics of the neural network performance. The network architecture is taken on the basis of the MNIST database experience. The eight-layered architecture having four convolutional layers is nearly best suitable for classifying small and medium size images. Image databases are formed of grayscale images whose size range is 28 × 28 to 64 × 64 by step 2. Except for the filter spatial extents, the rest of those eight layer hyperparameters are unalterable, and they are chosen scrupulously based on rules of thumb. A sequence of possible filter spatial extents is generated for each size. Then sets of four filter spatial extents producing the best performance are extracted. The rule of this extraction that allows selecting the best filter spatial extents is formalized with two conditions. Mainly, difference between maximal and minimal extents must be as minimal as possible. No unit filter spatial extent is recommended. The secondary condition is that the filter spatial extents should constitute a non-increasing set. Validation on MNIST and CIFAR- 10 databases justifies such a solution, which can be extended for building convolutional neural network classifiers of colour and larger images.

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Section: An Open Problem Of Setting Hyperparametersmentioning

confidence: 99%

Smooth Non-increasing Square Spatial Extents of Filters in Convolutional Layers of CNNs for Image Classification Problems

Romanuke

2018

Applied Computer Systems

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“…This result shows that any cut In what follows we aim at an analogous result using Hausdorff distance. Let us fix again the centres of the cut and squashing functions to be γ = δ so that the form of the cut function is c δ,δ , namely (3), whereas the form of the squashing function is s (β) δ,δ as given by (14). Both functions c δ,δ and s …”

Section: Approximation Of the Cut Function By A Squashing Functionmentioning

confidence: 99%

“…The equation was rediscovered in 1911 by A. G. McKendrick [35] for the bacterial growth in broth and was tested using nonlinear parameter estimation. The logistic function finds applications in an wide range of fields, including biology, ecology, population dynamics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, financial mathematics, statistics, fuzzy set theory, to name a few [12], [13], [11], [14], [18].…”

Section: Preliminariesmentioning

confidence: 99%

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

Илиев

Kyurkchiev²,

Markov³

2015

BIOMATH

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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.

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“…By the way, testing sets differ from training sets because it is sufficient to evaluate CEP only at the SDI maximum [15], [23], [28], [29]. …”

Section: Formalisation Of the 2lp Classifiermentioning

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

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-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.

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Approximation by network operators with logistic activation functions

Cited by 14 publications

References 23 publications

Smooth Non-increasing Square Spatial Extents of Filters in Convolutional Layers of CNNs for Image Classification Problems

Smooth Non-increasing Square Spatial Extents of Filters in Convolutional Layers of CNNs for Image Classification Problems

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

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