Module 6: Dimensionality Reduction
Lecture 29: Singular Value Decomposition (SVD)
How many dimensions to retain?
There is no easy answer
Concept of
energy
of a dataset
Total energy is sum of squares of singular values (aka
spread
or variance)
Retain
dimensions such that
of the energy is retained
Generally,
is between
to
In the above example,
= 1 retains
of the energy
Running time:
for
of size
and rank
dimensions such that 
of the energy is retained
is between 
to 
of the energy
for 
of size 
and rank 