Database Reference
In-Depth Information
9.4.6
Exercises for Section 9.4
entries in
U
or
V
to optimize first. Perform this first optimization step assuming we choose:
(a)
u
32
(b)
v
41
.
same value, what value minimizes the RMSE for the matrix
M
of our running example?
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
u
11
. Find its new best value, given the changes that have been
made so far.
(b) Then choose the best value for
u
52
.
(c) Then choose the best value for
v
22
.
EXERCISE
9.4.4 Derive the formula for
y
(the optimum value of element
v
rs
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 awar-
ded in September, 2009.
The NetFlix challenge consisted of a published dataset, giving the ratings by approx-
imately half a million users on (typically small subsets of) approximately 17,000 movies.
This data was selected from a larger dataset, and proposed algorithms were tested on their
ability to predict the ratings in a secret remainder of the larger dataset. The information for
