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Machine Learning Applied to Autonomous Vehicles 55

Figure 2. Neural Network with six inputs, one hidden layer with four nodes and one output.

Neural Networks

A neural network is a graph/network of mathematical functions. The graph/network
consists of neurons or nodes, and links or edges. It takes inputs and produces outputs.
Each node or neuron can be described as a mechanism that takes input from an input
layer or hidden layers and returns a result which is applied to other nodes or it becomes
an output node. For example, in Figure 2 the first layer (the inputs) are numerical values,
which are connected to each of the four nodes of the hidden layer. Similarly, each node
creates an output value which may be passed to nodes in the next layer. The output value
is returned from the output layer. The algorithm used to obtain the outputs knowing the
input and the parameters of each node are known as feed-forward due to the flow of
processing. In order to do that, it is necessary to define the order of operations for the
neurons. Given that the input to some neuron depends on the outputs of others, one needs
to flatten the graph of the nodes in such a way that all the input dependencies for each
node are resolved before trying to run its calculations. This is a technique called
topological sort. One example of this is the well known Kahn’s Algorithm (Kahn,1962).
To understand what the parameters of a node are, and how it is obtained, first it is
necessary to define the mathematical model of the node, which can be described by the
following equation:

= ∑ ( + ) (1)