Gain insights into basic and intermediate deep learning concepts, including CNNs, RNNs, GANs, and transformers. Delve into fundamental architectures to enhance your machine learning model training skills.

docker.tar.gz

Pytorch

GANS

This course is an accumulation of well-grounded knowledge and experience in deep learning. It provides you with the basic concepts you need in order to start working with and training various machine learning models. 

You will cover both basic and intermediate concepts including but not limited to: convolutional neural networks, recurrent neural networks, generative adversarial networks as well as transformers.

After completing this course, you will have a comprehensive understanding of the fundamental architectural components of deep learning. Whether you’re a data and computer scientist, computer and big data engineer, solution architect, or software engineer, you will benefit from this course.

Introduction to Deep Learning & Neural Networks


## The basic maths for processing graph-structured data

We already defined the graph signal $X \in R^{N \times F}$and the adjacency matrix $A \in R^{N \times N}$. A very important and practical feature is the  **degree** of each node, which is simply **the number of nodes** **that it is connected to**. For instance, every non-corner pixel in an image has a degree of 8, which is the surrounding pixels.


If $A$ is binary, the degree corresponds to the number of neighbors in the graph. In general, we calculate the degree vector by summing the rows of $A$. Since the degree corresponds to some kind of feature that is linked to the node, it is more convenient to place the degree vector in a diagonal $N \times N$ matrix:



import torch
#rand binary Adj matrix
a = torch.rand(3,3)
a[a>0.5] = 1
a[a<=0.5] = 0

def calc_degree_matrix(a):
 return torch.diag(a.sum(dim=-1))

d = calc_degree_matrix(a)

print("A:" ,a)
print("D:", d)


The degree matrix $D$ is fundamental in graph theory because it provides a single value of each node. It is also used for the computation of the most important graph operator: the graph Laplacian!


## The graph Laplacian

The graph Laplacian is defined as:

$$ L = D - A $$

In fact, the diagonal elements of $L$ will have the degree of the node if $A$ has no self-loops. On the other hand, the non-diagonal elements $L_{ij} = -1 \quad$ , when  $\quad i \neq j$ if there is a connection. If there is **no** connection, $L_{ij} = 0 , when \quad i \neq j$.

In practice:



# The basic maths for processing graph-structured data

We already defined the graph signal $X \in R^{N \times F}$and the adjacency matrix $A \in R^{N \times N}$. A very important and practical feature is the  **degree** of each node, which is simply **the number of nodes** **that it is connected to**. For instance, every non-corner pixel in an image has a degree of 8, which is the surrounding pixels.


If $A$ is binary, the degree corresponds to the number of neighbors in the graph. In general, we calculate the degree vector by summing the rows of $A$. Since the degree corresponds to some kind of feature that is linked to the node, it is more convenient to place the degree vector in a diagonal $N \times N$ matrix:




The degree matrix $D$ is fundamental in graph theory because it provides a single value of each node. It is also used for the computation of the most important graph operator: the graph Laplacian!


# The graph Laplacian

The graph Laplacian is defined as:

$$ L = D - A $$

In fact, the diagonal elements of $L$ will have the degree of the node if $A$ has no self-loops. On the other hand, the non-diagonal elements $L_{ij} = -1 \quad$ , when  $\quad i \neq j$ if there is a connection. If there is **no** connection, $L_{ij} = 0 , when \quad i \neq j$.

In practice:


Familiarize yourself with two major elements of graphs: graph Laplacian and eigenvalues.

Learn Deep Learning

Neural Networks

Training Neural Networks

Convolutional Neural Networks

Recurrent Neural Networks

Autoencoders

Generative Adversarial Networks

Attention and Transformers

Graph Neural Networks

Conclusion

Final Quiz

Mathematics for Graphs

The basic maths for processing graph-structured data

The graph Laplacian