Databases Reference
In-Depth Information
they explain the variance in the answers to the various questions—in
other words, they model the answers efficiently.
Our goal is to build a model that has a representation in a low dimen‐
sional subspace that gathers “taste information” to generate recom‐
mendations. So we're saying here that taste is
latent
but can be ap‐
proximated by putting together all the observed information we
do
have about the user.
Also consider that most of the time, the rating questions are binary
(yes/no). To deal with this, Hunch created a separate variable for every
question. They also found that comparison questions may be better at
revealing preferences.
Time to Brush Up on Your Linear Algebra if You
Haven't Already
A lot of the rest of this chapter likely won't make sense (and we want
it to make sense to you!) if you don't know linear algebra and under‐
stand the terminology and geometric interpretation of words like
rank
(hint: the linear algebra definition of that word has nothing to
do with ranking algorithms),
orthogonal
,
transpose
,
base
,
span
, and
matrix decomposition
. Thinking about data in matrices as points in
space, and what it would mean to transform that space or take sub‐
spaces can give you insights into your models, why they're breaking,
or how to make your code more efficient. This isn't just a mathemat‐
ical exercise for the sake of it—although there is elegance and beauty
in it—it can be the difference between a star-up that fails and a start-
up that gets acquired by eBay. We recommend
Khan Academy's
ex‐
cellent free online introduction to linear algebra if you need to brush
up your linear algebra skills.
Singular Value Decomposition (SVD)
Hopefully we've given you some intuition about what we're going to
do. So let's get into the math now starting with singular value decom‐
algebra
that we can always compose it into the product of three ma‐
trices as follows:
X
=
U SV
τ
