Dimensionality Reduction with Spark - Machine Learning with Spark - page 296

Relationship with matrix factorization
PCA and SVD are both matrix factorization techniques, in the sense that they decompose a
data matrix into subcomponent matrices, each of which has a lower dimension (or rank)
than the original matrix. Many other dimensionality reduction techniques are based on mat-
rix factorization.
You might remember another example of matrix factorization, that is, collaborative filter-
ing, that we have already seen in Chapter 4 , Building a Recommendation Engine with
Spark . Matrix factorization approaches to collaborative filtering work by factorizing the
ratings matrix into two components: the user factor matrix and the item factor matrix. Each
of these has a lower dimension than the original data, so these methods also act as dimen-
sionality reduction models.
Note
Many of the best performing approaches to collaborative filtering include models based on
SVD. Simon Funk's approach to the Netflix prize is a famous example. You can look at it at
http://sifter.org/~simon/journal/20061211.html .