Building Machine Learning Systems with Python - Richert, Coelho

Regression – Recommendations Improved
Using the binary matrix of recommendations
One of the interesting conclusions from the Netflix Challenge was one of those
obvious-in-hindsight ideas: we can learn a lot about you just from knowing which
movies you rated, even without looking at which rating was given! Even with a
binary matrix where we have a rating of 1 where a user rated a movie and 0 where
they did not, we can make useful predictions. In hindsight, this makes perfect sense;
we do not choose movies to watch completely randomly, but instead pick those
where we already have an expectation of liking them. We also do not make random
choices of which movies to rate, but perhaps only rate those we feel most strongly
about (naturally, there are exceptions, but on an average this is probably true).
We can visualize the values of the matrix as an image where each rating is depicted
as a little square. Black represents the absence of a rating and the grey levels
represent the rating value. We can see that the matrix is sparse—most of the squares
are black. We can also see that some users rate a lot more movies than others and
that some movies are the target of many more ratings than others.
The code to visualize the data is very simple (you can adapt it to show a larger
fraction of the matrix than is possible to show in this book), as follows:
from matplotlib import pyplot as plt
imagedata = reviews[:200, :200].todense()
plt.imshow(imagedata, interpolation='nearest')
The following screenshot is the output of this code:
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