Three-Layer Perceptron Position and Size Encoding in Shapes Classification Tasks

Abstract

This research reports on the ability of the three-layer perceptron trained with the backpropagation algorithm to solve classification tasks while encoding the spatial location, the size and the shape of two-dimensional geometrical figures in the Cartesian plane. The data set consists of images. The pixel’s brightness inside the shapes is kept constant and the remnant of the image is made of zero-valued pixels’ brightness. Results show that the neural network training based on backpropagation converges and the neural network classifier confirms the successfulness of the learning process with 100% correct classification rate. The hidden layer can successfully encode all the variables: position, shape, and dimension; and so, it does the output layer. Testing the three-layer perceptron with patterns not used for the learning process yields a correct classification rate between 95% and 100%. The task of encoding the shape of geometrical figures regardless of their size and their position on the Cartesian digital grid is regarded here as the ability of the three-layer perceptron to form complex decision regions. This ability is typical of this type of neural network because, with a sufficiently large hidden layer, it is a universal function approximator. The novelty of this paper is called Hidden Activation Analysis (HAA), and it consists of explicitly revealing that after the learning process the hidden layer of the three-layer perceptron can solve the pattern recognition task.