Grayscale Image Segmentation With Quantum-Inspired Multilayer Self-Organizing Neural Network Architecture Endorsed by Context Sensitive Thresholding

A method for grayscale image segmentation is presented using a quantum-inspired self-organizing neural network architecture by proper selection of the threshold values of the multilevel sigmoidal activation function (MUSIG). The context-sensitive threshold values in the different positions of the image are measured based on the homogeneity of the image content and used to extract the object by means of effective thresholding of the multilevel sigmoidal activation function guided by the quantum superposition principle. The neural network architecture uses fuzzy theoretic concepts to assist in the segmentation process. The authors propose a grayscale image segmentation method endorsed by context-sensitive thresholding technique. This quantum-inspired multilayer neural network is adapted with self-organization. The architecture ensures the segmentation process for the real-life images as well as synthetic images by selecting intensity parameter as the threshold value.

Asymmetric Sigmoidal Activation Function for Feed-Forward Artificial Neural Networks

Artificial neural networks of the feed – forward kind, are an established technique under the supervised learning paradigm for the solution of learning tasks. The mathematical result that allows one to assert the usefulness of this technique is that these networks can approximate any continuous function to the desired degree. The requirement imposed on these networks is to have non-linear functions of a specific kind at the hidden nodes of the network. In general, sigmoidal non-linearities, called activation functions, are generally used. In this paper we propose an asymmetric activation function. The networks using the proposed activation function are compared against those using the generally used logistic and the hyperbolic tangent activation function for the solution of 12 function approximation problems. The results obtained allow us to infer that the proposed activation function, in general, reaches deeper minima of the error measures and has better generalization error values.

Grayscale Image Segmentation With Quantum-Inspired Multilayer Self-Organizing Neural Network Architecture Endorsed by Context Sensitive Thresholding

A method for grayscale image segmentation is presented using a quantum-inspired self-organizing neural network architecture by proper selection of the threshold values of the multilevel sigmoidal activation function (MUSIG). The context-sensitive threshold values in the different positions of the image are measured based on the homogeneity of the image content and used to extract the object by means of effective thresholding of the multilevel sigmoidal activation function guided by the quantum superposition principle. The neural network architecture uses fuzzy theoretic concepts to assist in the segmentation process. The authors propose a grayscale image segmentation method endorsed by context-sensitive thresholding technique. This quantum-inspired multilayer neural network is adapted with self-organization. The architecture ensures the segmentation process for the real-life images as well as synthetic images by selecting intensity parameter as the threshold value.

A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function

The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can approximate an arbitrary continuous function provided that an unlimited number of neurons in a hidden layer is permitted. In this note, we consider constructive approximation on any finite interval of [Formula: see text] by neural networks with only one neuron in the hidden layer. We construct algorithmically a smooth, sigmoidal, almost monotone activation function [Formula: see text] providing approximation to an arbitrary continuous function within any degree of accuracy. This algorithm is implemented in a computer program, which computes the value of [Formula: see text] at any reasonable point of the real axis.

Logistic Regression Realized with Artificial Neuron and Estimation Formulas

In the paper an experiment is described, that was designed and conducted to verify hypothesis that artificial neuron with sigmoidal activation function can efficiently solve the task of logistic regression in the case when the explaining variable is one-dimensional, and the explained variable is binomial. Computations were performed with 12 sets of statistical parameters, assumed for the generation of 65356 sets of data in each case. Comparative analysis of the obtained results with use of the reference values for the regression coefficients indicated that the investigated neuron can satisfactory perform the task, with efficiency similar to that obtained with classical logistic regression algorithm, when the teaching sets of input data, corresponding with output values 0 and 1, do not allow for simple separation. Moreover, it has been discovered that the simple formulas estimating the statistical distributions parameters from the samples, offer statistically superior assessment of the regression coefficient parameters.

ON PERIODIC SOLUTIONS OF A TWO-NEURON NETWORK SYSTEM WITH SIGMOIDAL ACTIVATION FUNCTIONS

In this paper we study the existence, uniqueness and stability of periodic solutions for a two-neuron network system with or without external inputs. The system consists of two identical neurons, each possessing nonlinear feedback and connected to the other neuron via a nonlinear sigmoidal activation function. In the absence of external inputs but with appropriate conditions on the feedback and connection strengths, we prove the existence, uniqueness and stability of periodic solutions by using the Poincaré–Bendixson theorem together with Dulac's criterion. On the other hand, for the system with periodic external inputs, combining the techniques of the Liapunov function with the contraction mapping theorem, we propose some sufficient conditions for establishing the existence, uniqueness and exponential stability of the periodic solutions. Some numerical results are also provided to demonstrate the theoretical analysis.