@misc{10481/76426,
year = {2022},
url = {http://hdl.handle.net/10481/76426},
abstract = {Nowadays, neural networks have represented a great step forward in the area of computing
and artificial intelligence. We have been provided with different ways to, through mathematics
in conjunction with some powerful computational tools, recognize patterns in images,
classify images or even solve optimization problems. For this reason, this Final Degree Project
approaches this field of neural networks through mathematical tools, despite the fact that it
uses the necessary computation for its proper function. Also, the area of neural networks is
still booming and research continues to maximize their use, although it has been proven that
they are quite useful in all scientific and non scientific areas.
In chapter 1 we will explain advances in current neural networks and examples of research
articles in which you can appreciate the latest on neural networks (in this case generative
adversarial networks that will be introduced later). In addition, we explain the historical
process of neural networks and a way to compute the error produced by the neural network
using a error function. Like any error function, the ultimate aim is to minimize a certain
error function and find what values the variables should have so that the error is the minimum.
This problem cannot be solved by basic optimization techniques and, therefore, more
advanced optimization methods should be used, such as iterative methods like gradient
descent, stochastic gradient descent or Adam method.
In chapter 2, we will go deeper into these optimization methods and we will see certain
convergence results along with their respective proofs. These optimization methods have
a disadvantage; they need to know the gradient of the function to which it is applied. For
this reason, the backpropagation algorithm has also been detailed, which is an iterative
method that will provide us with the partial derivatives of the error function with respect
to any weight and bias of the neural network. To do this, the 4 fundamental equations of
backpropagation will be enunciated and demonstrated. Finally, it will be explained how they
are used to find the gradient of the function.
In chapter 3, we will introduce convolutional neural networks and explain them through a
practical example. In addition, we will use a code from Tensorflow in Python programming
language to be able to classify clothing images using convolutional neural networks.
Finally, in chapter 4, a Python code from the book Neural Networks and Deep Learning
will be used to recognize handwritten characters through artificial neural networks and to
see, in practice, the theory explained in Chapters 1 and 2. Furthermore, we will be able to
check how the neural network is able to train itself automatically and to produce a better
output with the least error possible.},
title = {Introducción a las redes neuronales para el tratamiento de imágenes},
author = {Santillana Quesada, Samuel},
}