Building Machine Learning Systems with Python - Richert, Coelho

Regression – Recommendations Improved
Now we can use this in several ways. A simple one is to select the nearest neighbors
of each user. These are the users that most resemble it. We will use the measured
correlation discussed earlier:
def estimate(user, rest):
'''
estimate movie ratings for 'user' based on the 'rest' of the
universe.
'''
# binary version of user ratings
bu = user > 0
# binary version of rest ratings
br = rest > 0
ws = all_correlations(bu,br)
# select 100 highest values
selected = ws.argsort()[-100:]
# estimate based on the mean:
estimates = rest[selected].mean(0)
# We need to correct estimates
# based on the fact that some movies have more ratings than others:
estimates /= (.1+br[selected].mean(0))
When compared to the estimate obtained over all the users in the dataset, this
reduces the RMSE by 20 percent. As usual, when we look only at those users that
have more predictions, we do better: there is a 25 percent error reduction if the user
is in the top half of the rating activity.
Looking at the movie neighbors
In the previous section, we looked at the users that were most similar. We can also
look at which movies are most similar. We will now build recommendations based on
a nearest neighbor rule for movies: when predicting the rating of a movie M for a user
U, the system will predict that U will rate M with the same points it gave to the movie
most similar to M.
Therefore, we proceed with two steps: first, we compute a similarity matrix (a matrix
that tells us which movies are most similar); second, we compute an estimate for
each (user-movie) pair.
We use the NumPy zeros and ones functions to allocate arrays (initialized to zeros
and ones respectively):
movie_likeness = np.zeros((nmovies,nmovies))
allms = np.ones(nmovies, bool)
cs = np.zeros(nmovies)
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