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Implementing a Neural Network from Scratch - An Introduction
In this post we will implement a simple 3-layer neural network from scratch. We won't derive all the math that's required,
but I will try to give an intuitive explanation of what we are doing and will point to resources to read up on the details.
In this post I'm assuming that you are familiar with basic Calculus and Machine Learning concepts, e.g. you know
what classification and regularization is. Ideally you also know a bit about how optimization techniques like gradient
descent work. But even if you're not familiar with any of the above this post could still turn out to be interesting ;)
But why implement a Neural Network from scratch at all? Even if you plan on using Neural Network libraries
like PyBrain in the future, implementing a network from scratch at least once is an extremely valuable exercise. It
helps you gain an understanding of how neural networks work, and that is essential to designing effective models.
One thing to note is that the code examples here aren't terribly efficient. They are meant to be easy to understand. In
an upcoming post I will explore how to write an efficient Neural Network implementation using Theano..
In [1]:
# Package imports
import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
import matplotlib
# Display plots inline and change default figure size
%matplotlib inline
matplotlib.rcParams['figure.figsize'] = (10.0, 8.0)
Generating a dataset
Let's start by generating a dataset we can play with. Fortunately, scikit-learn has some useful dataset generators, so
we don't need to write the code ourselves. We will go with the make_moons function.
In [2]:
# Generate a dataset and plot it
np.random.seed(0)
X, y = sklearn.datasets.make_moons(200, noise=0.20)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)
Out[2]:
<matplotlib.collections.PathCollection at 0x110609f50>
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