Introducción a las redes neuronales para el tratamiento de imágenes
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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.