How to build a three-layer neural network from scratch

In this post, I will go through the steps required for building a three layer neural network. I'll go through a problem and explain you the process along with the most important concepts along the way. A farmer in Italy was having a problem with his labelling machine: it mixed up the labels of three wine cultivars. Now he has 178 bottles left, and nobody knows which cultivar made them! To help this poor man, we will build a classifier that recognizes the wine based on 13 attributes of the wine.