# Month: February 2014

## Neural Networks, Part 3: The Network

We have learned about individual neurons in the previous section, now it’s time to put them together to form an actual neural network.

The idea is quite simple – we line multiple neurons up to form a layer, and connect the output of the first layer to the input of the next layer. Here is an illustration:

Each red circle in the diagram represents a neuron, and  the blue circles represent fixed values. From left to right, there are four columns: the input layer, two hidden layers, and an output layer. The output from neurons in the previous layer is directed into the input of each of the neurons in the next layer.

We have 3 features (vector space dimensions) in the input layer that we use for learning: $$x_1$$, $$x_2$$ and $$x_3$$. The first hidden layer has 3 neurons, the second one has 2 neurons, and the output layer has 2 output values. The size of these layers is up to you – on complex real-world problems we would use hundreds or thousands of neurons in each layer.

## How to normalise feature vectors

I was trying to create a sample file for training a neural network and ran into a common problem: the feature values are all over the place. In this example I’m working with demographical real-world values for countries. For example, a feature for GDP per person in a country ranges from 551.27 to 88286.0, whereas estimates for corruption range between -1.56 to 2.42. This can be very confusing for machine learning algorithms, as they can end up treating bigger values as more important signals.

To handle this issue, we want to scale all the feature values into roughly the same range. We can do this by taking each feature value, subtracting its mean (thereby shifting the mean to 0), and dividing by the standard deviation (normalising the distribution). This is a piece of code I’ve implemented a number of times for various projects, so it’s time to write a nice reusable script. Hopefully it can be helpful for others as well. I chose to do this in python, as it’s easies to run compared to C++ and Java (doesn’t need to be compiled), but has better support for real-valued numbers compared to bash scripting.