Module 6: Dimensionality Reduction
Lecture 33: Embedding
Johnson-Lindenstrauss lemma
Embedding
(
mapping
)
of
points from
to
where
with distortion at most
Randomized construction
Construct
vectors
where each component
is chosen from a standard normal distribution
Object
is then mapped to
where
Then, for two objects
and
, with very high probability,
i.e.,