9.5. THE NETFLIX CHALLENGE
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Exercise 9.4.3: Starting with the U and V matrices in Fig. 9.16, do the
following in order:
(a) Reconsider the value of u11. Find its new best value, given the changes
that have been made so far.
(b) Then choose the best value for u52.
(c) Then choose the best value for v22.
Exercise 9.4.4: Derive the formula for y (the optimum value of element vrs
given at the end of Section 9.4.4.
Exercise 9.4.5: Normalize the matrix M of our running example by:
(a) First subtracting from each element the average of its row, and then
subtracting from each element the average of its (modiﬁed) column.
(b) First subtracting from each element the average of its column, and then
subtracting from each element the average of its (modiﬁed) row.
Are there any diﬀerences in the results of (a) and (b)?
9.5
The Netﬂix Challenge
A signiﬁcant boost to research into recommendation systems was given when
Netﬂix oﬀered a prize of $1,000,000 to the ﬁrst person or team to beat their
own recommendation algorithm, called CineMatch, by 10%. After over three
years of work, the prize was awarded in September, 2009.
The Netﬂix challenge consisted of a published dataset, giving the ratings by
approximately half a million users on (typically small subsets of) approximately
17,000 movies. This data was selected from a larger dataset, and proposed al-
gorithms were tested on their ability to predict the ratings in a secret remainder
of the larger dataset. The information for each (user, movie) pair in the pub-
lished dataset included a rating (1–5 stars) and the date on which the rating
was made.
The RMSE was used to measure the performance of algorithms. CineMatch
has an RMSE of approximately 0.95; i.e., the typical rating would be oﬀby
almost one full star. To win the prize, it was necessary that your algorithm
have an RMSE that was at most 90% of the RMSE of CineMatch.
The bibliographic notes for this chapter include references to descriptions
of the winning algorithms.
Here, we mention some interesting and perhaps
unintuitive facts about the challenge.
• CineMatch was not a very good algorithm. In fact, it was discovered early
that the obvious algorithm of predicting, for the rating by user u on movie
m, the average of:
