Book Image

Hands-On Mathematics for Deep Learning

By : Jay Dawani
Book Image

Hands-On Mathematics for Deep Learning

By: Jay Dawani

Overview of this book

Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL.
Table of Contents (19 chapters)
1
Section 1: Essential Mathematics for Deep Learning
7
Section 2: Essential Neural Networks
13
Section 3: Advanced Deep Learning Concepts Simplified

Facial recognition in 3D

Let's go ahead and see how this translates to a real-world problem such as 3D facial recognition, which is used in phones, security, and so on. In 2D images, this would be largely dependent on the pose and illumination, and we don't have access to depth information. Because of this limitation, we use 3D faces instead so that we don't have to worry about lighting conditions, head orientation, and various facial expressions. For this task, the data we will be using is meshes.

In this case, our meshes make up an undirected, connected graph, G = (V, E, A), where |V| = n is the vertices, E is a set of edges, and contains the d-dimensional pseudo-coordinates, , where . The node feature matrix is denoted as , where each of the nodes contains d-dimensional features. We then define the lth channel of the feature map as fl, of which the ith node...